I sympathize with your situation. Some people aren't too bothered by their appearance one way or another. For many, though, a feature that's outside the norm--whether it's a misshapen nose, huge breasts or ears that stick out--can be a real challenge. People can be very unkind, especially at your age, and self-esteem can suffer.
At the same time, I also understand what your parents might be thinking. As your looks change, it's possible your ears may not seem as prominent (though your ears won't change and most people don't "grow into" their ears). Your parents may think that as you get older, you will feel less sensitive. Again, it's possible that your feelings won't seem as acute with time, but it's also likely your dissatisfaction won't disappear.
I suggest you prepare a case to present to your parents. You can print out articles on bullying to show them. You can also look for relevant articles on teen self-esteem. Sit down and talk with them openly about how you are feeling, but also ensure that your approach and the information you present is rational and objective. Consider whether there's anything you can do to help with the cost of otoplasty, which on average is about $3500 for the surgeon (plus other fees such as the anesthesiologist and facility charges). Could you perform extra chores and save money to cover the cost of an initial consultation? Would your parents be interested in learning about financing options and could you contribute some money each month to paying off surgery over time?
If they are adamant that they will not consider surgery, you can make otoplasty your goal and arrange for the procedure at age 18. Having surgery as something to work toward may help you get through the next few years. (And who knows? Your parents may come around when they see your determination.)
Good luck to you,
Elliot Jacobs, M.D.
New York Plastic Surgeon