There are several issues to review...
First of all, at 16 it is likely you may experience some further growth of your breasts, and that if this happens after you had breast reduction surgery, that a second surgery to further reduce and improve their shape would be a more risky endeavor not likely to be covered by your health insurance.
The question of insurance coverage of the initial procedure is very much a regional one, and therefor would best be answered by a plastic surgeon in your community. Unfortunately, the insurance companies make these decisions in a very arbitrary way and there is no predictability to the process. The only way to know if your surgery might be covered is to try to get it covered... and even after you have surgery, there's no guarantee your surgeon will actually be paid (but that's another story).
My recommendation to young women like yourself is to wait as long as you can before surgery, as this is definitely one you only want to have to have once- not because it is very painful, because it usually isn't, but in order to minimize the risk of complications should a second one be necessary.