My insurance considers septoplasty a cosmetic procedure and will not cover it. What is the out-of-pocket cost in NY? (Photo)

I have every symptom of a deviated septum. I sleep on one side, get nosebleeds, minor sinus infections, and I even have a small callus in my nose where the cartilage protrudes. However, most of the visible deviation is just in the size of my nostrils. I am fed up with daily discomfort, but I have student insurance with United healthcare. I can pay no more than $9,000 for the procedure out-of-pocket. How can I cut costs and still get good results from a good doctor?