Nose surgery cannot lower your nostrils
The short answer to your question is no, it is not possible to lower the nostrils. However, you may want to go to a Plastic Surgeon who does computer imaging and see how you would look like if your nasal tip was slightly elevated and narrowed.
The tip can be raised slightly without creating a pig nose.
When the tip of the nose is long over the lip, it can be raised. How much will depend on how much upper lip length you have already and how much the tip is raised. If the upper lip is already "too long" then the surgeon should be conservative in raising the tip.
"Lowering the nostrils" is difficult and leaves a scar, so you will be trading something natural (long upper lip) for something unnatural (scar) and this is usually a "bad trade".
Rhinoplasty and the Nostrils
It is very difficult to answer you question despite your detailed description of your nose and your wishes. It would be most helpful to see pictures of your nose in the following views: frontal, profile, 3/4's, and from below the nostrils.
Nostril size and position can be changed, but your nose needs to be examined by an experienced rhinoplastic surgeon who could then tell you what to expect, and most importantly whether your expectations and goals could be reasonably met.
Good luck and be well.
Changing the Tip of The Nose
Based upon your photograph, it seems your request is reasonable. It certainly is possible to make the tip less boxy and reduce the nose to be more proportionate to your face, without creating a "pig-like" appearance with excessive show of the nostrils.
Of course, a full examination during consultation is needed to be sure. See a well qualified Rhinoplasty surgeon for consultation.
Move nostril position versus upper lip lift
If the goal is to achieve a shorter upper lip, then there is a special procedure that accomplishes this- called the upper lip lift. However, there are techniques to move the position of the nostrils, but it may not be the best way to achieve the look you are seeking.
Changing the nostrils and the tip in rhinoplasty
You pose a good question, but one that can't be answered properly without seeing you in person. Yes the position and the size of the nostrils can change relative to other structures. The issue with you seems to be that you'd rather lower your nostrils rather than raise the tip b/c you're afraid your nose will be too turned up.
My advice to you would be to visit with us to discuss your concerns. From the picture it seems as if your nasal length is fine and you may not even need surgery. Sometimes computer imaging can help in the discussion. I'm always wary when a patient tells me they want some changes but "are afraid of..."
Many techniques exist to help one achieve a more pleasing aesthetic result
Many techniques exist to help one achieve a more pleasing aesthetic result. This includes changing or altering the appearance of the tip and nostrils. It is best for you to seek a consultation with a rhinoplasty surgeon and have him or her give you their opinion as to what can be achieved with your nose.
It is possible to change the relationship between your nostrils and tip
Rhinoplasty is a popular and effective surgery to recontour the shape of your nose. During the surgery, there are many techniques that a surgeon can perform to alter the different parts of your nose. It is possible to change the shape of your tip and nostril to create the effect that you are looking for.
Your best bet is to work with a board-certified plastic surgeon who has a great deal of experience with rhinoplasty and cartilage techniques as you may need a small cartilage graft to help retain the new shape.