Can a 15 year old get a breast reduction?

I'm sorry to hear about the physical and psychosocial problems your disproportionately large breasts are causing you. 
It is probable that you are dealing with juvenile breast hypertrophy along with the physical and psychosocial consequences of this diagnosis. In other words, the breasts are too large for your frame causing  both physical and psychological distress.
In my practice, timing of breast reduction surgery is determined on a case-by-case basis. It is not too early to do your homework and learn as much as possible  about  breast reduction surgery and the potential risks and complications associated with  the procedure.  Hopefully you have the support of your parents as you do your homework.
Unsatisfactory scarring is  one of the potential complications. Make sure you also understands that further surgery may be necessary in the future (for example if the breasts were to grow in size again).
On the other hand, breast reduction surgery is one of the most patient pleasing operations we perform and I think that for the right teenager (enough symptoms) it may be an excellent option (regardless of the age).
Sometimes breast  reduction surgery is covered through health insurance. The best way to obtain insurance coverage for breast reduction surgery involves some “hoops” to jump through. The more documentation you have (for example, from your primary care doctor, physical therapist, chiropractor etc.) the better when it comes to obtaining insurance “authorization” for the procedure.
This documentation and letter/pictures from your plastic surgeon will help you obtain authorization.
 When the time is right,  seek consultation with well-trained/experienced board-certified plastic surgeons.

I hope this,  and the attached link, helps.

Considerations for young woman with large breasts;Typically breasts stop growing one year after the onset of a girls period. To be safe we consider breast reduction surgery, one year after the stop of breast enlargement.Are you ready? young girls have different expectations than a full grown adult. All surgery has some degree of risk and pain. Young woman should understand that not all surgery is successful and that secondary surgeries and complications may arise.Will it change my life? Another issue for young woman is the idea that it will be a life changer. Well, physically it certainly will make life much easier, but emotionally, you are still who you are and no degree of surgery will change how you interact with others or how your friends deal with you.To learn everything else that you need to consider, please read my book " Cosmetic Breast Surgery - A complete guide from A to double D".Good luck!