The same thing applies to protruding ears, large noses, and even large breasts, though insurance coverage is sometimes obtainable for breasts large enough to exceed certain height/weight guidelines.
But, tuberous breasts are generally considered "cosmetic" in nature by most insurance companies. You should see one or more ABPS-certified plastic surgeons in New York who can tell you honestly what your chances are of obtaining coverage. Truthfully, I would expect them to be low. I practice in Minnesota, the home of HMOs and health-care insurers, and have been a reviewer for Blue Cross/Blue Shield and Medicare for years--this would not be a "covered" expense, even with appeals.
So, be prepared to pay, but that means you get to choose the expert plastic surgeon who you want to do your surgery. Interview carefully, and choose wisely, so your result is good and you are happy. . . otherwise, you may end up having additional reconstructive work (that may or may not be covered as well) to correct poor initial surgery! For examples see cases 1 and 3 via the link below. Best wishes!