Is it possible to correct the bone in my nose and lower the angle so the skin between nose and lip doesn't look so tense?(photo)

The recently popular concept of tension nose is not as simple as the mere excess of nasal spine bone and removing it, there are different subvarieties and considerations.
It is true, above any "tension" concept, your nose is one with the following features which prevail as main issues to be addressed:
-short nose and short septum: the distance between radix (top of nose) and tip is the one considered to tag a nose as long, short or balanced, yours is short; this shortness can be due to a series of factors, one, more or a mixture, in your case the caudal septum is very short but not all of it, your atypical case has well developed caudal septum next to the maxilla but too short near the tip, leading to the abnormal nasolabial angle you have and the unsighty upturned tip, which is a MUST do; no one option or plan for your nose may ignore or jump across lengthening this specific part of the caudal septum, graft it and correct your upturned nose; I warn you about this because very few surgeons will detect this paramount importance issue and way lesser will have skills or passion to correct it; not correcting this issue would let to a catastrophic nasal collaps and loss of support like a piggy and grotesque nose; the treatment is delicate and tedious, by means of grafting the septum and eventually a so called shield graft (en bloc tip-columella custom tailored fragment)
-alar rim retraction: do research about this; now this issue is NON APPARENT, so beware again! poorly experienced surgeons will not even notice this issue, why so? because the alae and the nostril rims are as angled upwards and over rotated as the columella-caudal septum... so both, columella and alar rim, stay parallel and in good balance... however, once the nasolabial angle of the columella is lowered the nostrils will stay at the angle they are now leading to hug nostrils, septal mucosa exposure and then, only then, the alar rim retraction will be noticeable; correction of this issue is also A MUST, and has to be planned according to the grade of lowering of the columellar angle, by means of caudal extension batten graft of the lateral cruras, eventually with rim grafting
-your tip looks cute and in good side shape and size, however I may change my opinion based on the frontal view, obviously your opinion counts in the end, but so far your tip shape and size looks fine from the side
-overally you need a bit, only a bit, of dorsal bump shaving and lowering the dorsum, associated with the mandatory osteotomies to close the roof
-a bit of tip deprojection is also needed to balance your tip with the shaven dorsum, which is of PARAMOUNT importance in your case for reasons you'll read below
And now, let's go to the "tension nose" concept...
The tension nose is a recent fashing or trending topic in rhinoplasty which I don't like very much as terminology... "tension"? which tension? I mean... what do we intend to refer to when we say tension... essentially this term has been applied in the recent years by some "posh" surgeons to the noses in which the patient has what we always have called as "prominen nasal spine"... just it, and if the nasal spine is prominent can be trimmed, sure, but... enhancing such simple concept into a "kind of nose" is, IMHO, far fetched, but well... trends are trend... and marketing is nowadays passion on the Internet... but things are as they are.
Also "tension noses" are those of a bit of ethnicity, arab or jewish backgrounded most of them, in which the nasal tip is under downwards tension... and this kind of "tension" has had always a name: SHORT COLUMELLA SYNDROME, a very conflictive and problematic issue; let me explain on.
When the columellar sekeleton (medial crura or pillars) is of normal length but the columellar skin is short, when there is a tension due to a shorfall of columellar skin then the tip is bent downwards and acquires a very tipical shape, because the skin literally bends and warps the medial cruras; this kind of nose has especific treatment (columellar strut, tongue in groove, etc..., even in asian noses columellar flaps to lengthen the columellar skin).
The association of a shortfall in columellar skin and normal or weak medial cruras leads to a "tension nose" with down and inwards pull on the tip and a very specific shape, okay... but... what if the medial cruras are strong, made by thick and firm cartilages? how will the shortfall of skin affect the nose? Well, the answer is YOUR nose: the nasolabial angle is webbed.
If there is a columellar shorfal of skin but the skin is unable to beat the structural support of the underlying medial cruras then... the cruras pull up the skin from the philtrum (space between nose and upper lip) recruiting the required skin to cover them (in males I have seen hairy moustache bear into the initial milimitres of the columella, literally the patient had to shave part of the columellar skin)... so short columellar skin cover... instead of pulling down the tip, literally and physically pulls up the filtrum but makes a webbed effect or a fussion effect between columella and philtrum, DELETING THE NASOLABIAL ANGLE or at least smoothening it a lot.
UNEXPERIENCED surgeons may all say at once "oh you see? a tension nose with too prominent nasla spine... let's trim that bony prominence", but old foxes we do know this is not always the solution.
A smoothened or deleted nasolabial angle maybe, therefore, due to 2 reasons:
-a prominent nasal spine, then the solution is trimming that tiny bone
-or a short columellar skin envelope in a context of strong medial cruras and webbed nasolabial angle, and the solution is local plasties (columellar lengthening flaps or just a simple zetaplasty) to supply a few milimitres of skin; however, may the nose undergo a certain amount of tip deprojection (never just due to this webbed skin, only if it is anatomically and aesthetically indicated) this commonly SUFFICES to get rid of the... "tension", or help to use more conservative methods of skin supply to the columella.
How to tell if is is a prominent nasal spine or a webbed nasolabial angle, decision and diagnosis which will fully condition or determine the final technical option for its treatment? Well, firstly by the simple look of the problem... obviously this is not for lay eyes or for not well experienced surgeons, but from how you look I'd bet you are not a prominent nasal spine case, why do I think so? because where your webbed nasolabial angle happens to be there is NO nasal spine! the nasal spine is at the very right base of the nasal fossa opening, and your webbed nasolabial angle is way lower.
Anyhow, the final and undisputable diagnostic test is one that you, as patient and lay in rhinoplasties, may perform... touch it! if you can reduce, depress and flatten the web by pushing or it or... much better.. pushin up the filtrum to "supply skin" and reduce the "tension" and you are able to make the web disappear building a well defined nasolabial angle... means I was right guessing yours is not a prominent nasal spine case; should it be otherwise then I am wrong and your nasal spine needs removal.
Most surgeons will ignore this critical issue (and other afore mentioned) or simply attribute it to a tension nose due to nasal spine prominence (ahhh fashion victims...), but the truth is your nose is, well likely, another kind of "tension" grounded not on the bony excess but on the shortfall of skin... so beware.
Please... let us publicly know the results of your test. If you can manually build a well defined angle and get rid of the web by means of pushing it in, pushing-shortening the tip or pushing up the philtrum... then the bone is not the cause. 
Needless to say your nose is a collection of pitfalls, a mine field for not a well trained, well experience, knowledgeable and very observative surgeon; difficulty, therefore, is 10 out of 10 scale in primary noses, due to the high end techniques required (septal lengthening, alar rim caudal grafting, etc), the fine calibration required and the difficulty for the mere diagnosis. Do research well about surgeon's capacitation to carry out your nose successfully. Surgical time 4-5 hours.
If you wish better grounded opinion please do post or send privately well lit, focused and standard images: frontal, both lateral and both oblique views, also underneath the nostrils.
Feel free to request any additional information from me.

Click on the "Web reference" link, just below my response, or go here:
FacialSurgery.com/RealSelf/RealSelf_evagc29.html
I made a computer morph of your nose, and an animation of the morph, to show the changes that are possible for your nose in truly expert hands.The reason that your upper lip skin seems tense is that your nose is strong in its forward projection away from your face. If you take anyone's nose, and pull it forward away from the face, the upper lip skin will follow the nose and be pulled forward.In the morph, I brought the tip of your nose back closer to your face. If you look in the animation at the junction between the upper lip and the bottom of the nose, you'll see that the upper lip skin moves back as the tip of the nose moves back. Moving the tip back closer to the face, reducing it's forward projection, is called "de-projecting" the nose.The woman in the short video above had her nose de-projected.You'll also see that I didn't lower the position of the tip. When the lip comes back, and when the tip of the nose comes back, it makes the nose *look* longer, so you really don't need to have the tip of the nose lowered. In the animation, hopefully in the "after" view, your nose doesn't look as shorty to you. In any case, lowering the tip is a very very difficult operation, and it doesn't always work as well as we'd like, and I like to avoid it when I can.Fascinating how different doctors will give hugely different opinions about the same concern. At the time I'm writing this, there are two other answers posted to your question, and IMHO I think they both miss the mark completely. I won't go into detail here online about that.
You should understand that the changes I demonstrated in the morph require advanced techniques, techniques that most plastic surgeons cannot handle.  Be sure to read the section in the "Web reference" link on how to stay out of trouble while searching for a rhinoplasty surgeon. You should only have surgery if you are able to make yourself very confident in your surgeon's skills.
I'd love to hear what you think of the morph. Did it seem to address your main concerns?
Your nose is also a good example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. When you see his goals, you'll know whether he has an eye for a beautiful nose, and whether he shares your opinion of what constitutes a beautiful nose. You'll also know whether the changes he proposes are enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. But remember, you're not hiring him for his skills with the computer. The doctor must then show you his before and after photos to prove that he can actually accomplish what he draws on the computer.
In your case in particular, you need to find a surgeon who understands all of the issues I mentioned, and how they fit together, and who can actually accomplish them in surgery. 

You have a prominent anterior nasal spine which pushes up against your nasolabial angle creating the tension that you see. During your rhinoplasty the anterior nasal spine can be reduced to decrease the nasolabial angle and subsequently relieve the tension that you see.

evagc29,
Thanks for the question and picture.  You appear to have a tension nose deformity, which is caused by your maxillary spine, which is a bone that your septum attaches to (you can feel it between your two front teeth and your nose).  The maxillary spine is "pushing" the other structures of your nose up, and your lip is following it.  An open rhinoplasty by a well trained, experienced surgeon should be able to give you a look that you are happy with.  Good luck!

This, strictly speaking, is not a nose issue. It is an issue of the tissue just beneath the nose. That tissue can be modified and create a better transition between the lip and the nose. This may require some manipulation of the maxillary bone.All the best,Talmage Raine MD