Is it possible to get surgery to make my nostrils smaller? (Photo)

A rhinoplasty would be a nice option for you.  It would reduce the dorsal hump and nasal projection and in the process reduce the visibility of your nostrils.  A nostril width reduction may not be necessary after the dorsum and tip are addressed. 

Click on the "Learn more" link, just below my response, or go here:
FacialSurgery.com/RealSelf/RealSelf_brycekathleen.html
I made a computer morph of your nose, and an animation of the morph, to show the changes that could be possible for your nose in truly expert hands.You'll see, perhaps best in the animation, that I lowered the bump on the bridge, and I brought the tip back closer to your face. I made the bridge just the teeniest bit concave, because that's a feminine feature, and your nose doesn't need a huge change. From the front it looks great.
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 "Learn more" 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. Read that page very carefully. Most plastic surgeons are quite poor at this operation, and I believe my advice will go a long way toward keeping you safe.
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 an attractive nose, and whether he shares your opinion of what constitutes an attractive 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. 

Based on your photos-you appear to be good candidate for Rhinoplasty, preferably through a closed technique- without a scar across your columella. In the right hands, I predict you should expect a more elegant and feminine nose. 

Thank you for your question. It is very difficult to make an informed recommendation from these pictures.  You have to be careful to narrow the base of the nose, when you have retracted nostrils and over-rotation.  You may want to address the relationship of the nostril to the base of the nose instead.  Please seek the advice of a double board certified Plastic Surgeon of the face.

However, sometimes the nostrils only appear to be too wide or flare. When the tip is too narrow, pinched or has deep creases that extend to the nostril rim, the nostrils may appear to flare too much yet might be of normal width. The treatment is then to support the nostril rims with grafts. The tip will actually look more refined and the nostrils less flared. It is impossible to tell what makes your nostrils look too wide from the photo posted since there is no view from below.

Hello! After evaluating your case, you are a candidate for a rhinoplasty. In relation to your nostrils, these can be reduced with the resection of a small portion of tissue in the base (internal) of the nose to obtain an attractive result. Be sure to contact a certified plastic surgeon to make a correct and safe assessment.We hope this help clarify your doubt on the subject.
-Dr. Alexandrish Karvendrish Rodríguez Tavárez

Hello and thank you for your question. Based on your
photograph, you may benefit from a tip refining rhinoplasty which can be designed to make your nostrils smaller.  You may also benefit from a dorsal hump
reduction.  Make sure you specifically look at
before and after pictures of real patients who have had this surgery performed
by your surgeon and not just a computer animation system.
The most important aspect is to find a surgeon you are comfortable with. I
recommend that you seek consultation with a qualified board-certified plastic
surgeon who can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D. FACS
Harvard-trained plastic surgeon

I strongly encourage you to see a rhinoplasty expert for a consultation as only limited recommendations can be made on this forum. It appears that the top 2/3 of your nose are slightly too narrow for you nasal tip, which is a little wide and bulbous. You also have a dorsal hump and tension tip. The skin thickness plays and important role as to what can be realistically achieved and what can't. I suspect your skin is medium in thickness or even on the thicker side. With all that said, if you are otherwise healthy and have realistic expectations, you would be an excellent candidate for a rhinoplasty to improve nasal refinement. Hope that helps. Good luck!

At the conclusion of most rhinoplasty procedures, it is time to check the nostrils and see if there is excess size or flare. You seem to have a lot of flare, which can be changed by excising some skin and soft tissue at the base of the nose, next to the natural crease where it can be hidden. There are other factors with your nose which can also be changed with a carefully planned rhinoplasty operation. This should all be addressed during a consultation with an experienced rhinoplasty surgeon. 

I would recommend starting with a consultation with a board certified facial plastic surgeon that specializes in rhinoplasty surgery. 
I would recommend writing down the following questions before scheduling your consultation:
1. Are you unhappy with the tip of your nose? 
2. Do you feel that your nose is too wide? 
3. Do you want to make your nostrils smaller in appearance? 
4. Are you looking to decrease the general size of your nose?
I hope some of these questions will help you pinpoint what it is that you don't like about your nose. I wish you the best as you research your options when scheduling a rhinoplasty consultation.
Sincerely,
Philip J. Miller, MD, FACS Double Board Certified Facial Plastic Surgeon