I can't see my nostrils from the side. Is there any way to reduce the size? (Photo)

In your situation, it's usually not about reducing the nostril size, but instead improving the length of the columella, the cartilage in the midline of the nose. There are grafts that can be placed to create a better relationship between the two. Be sure to see an experienced rhinoplasty surgeon to discuss the options.

The issue that you alluding to in your comments is poor columella show.  You have very thick alar skin and the portion of your nose that sits between your nostrils is called the columella.  Typically, 2-3 mm of the columella can be seen on profile.  I suspect that you do not have a great deal of tip support either.  Often times, placing a graft of cartilage, a columella strut, can help increase columella show and improve tip support.  Altering the nostrils is not very effective in addressing this issue.  Thick skin, which you have, also makes improvement a bit less dramatic but improvement can certainly be achieved.

You have alar flare and hooding. There are a few ways to approach this. But it's important to remember that with thick skin, you have to have realistic expectations about how much definition of the nostrils can be achieved. Some possibilities of correcting this problem are bringing out your columella, alar base reduction, and a z-plasty. You might need some combination of these options also. Sometimes, an intranasal mucosal excision can also help to bring the nostril edge upwards. Good luck! 

Without more photos, and best an exam in person, it is difficult to say what coudl be done. Good luck.