I am sorry to hear that you are dealing with this at such a young age. Breast reduction could be a possibility. However, you definitely want to be as educated as possible and understand the risks of having this surgery at such a young age. Generally, we prefer patients to be at least 16 or at an age where growing is done or stable. It is important to weigh your options. While a reduction may get rid of some of your medical and emotional problems, you are also left with scars and the possibility of not being able to breast feed. This may not be important to you right now, but it may if you decide to have children. It is possible that you may need another surgery down the road since you are most likely not done growing, but then again you may not. These are all things to consider. Have a consultation with a board certified plastic surgeon and your parents and really make sure that it is something you are ready for.
As for insurance covering the procedure, this will depend on several factors. Your reduction will have to be determined medically necessary. You will need evidence to back that up for example back, neck, or shoulder pain, indentations from your bra straps, skin irritation underneath your breasts, restriction of physical activity due to the weight and size of your breasts, etc. It will also depend on the amount of breast tissue that is removed. Every insurance is different, but you can always check with your specific insurance to see what they will potentially cover. If they won't cover the procedure, depending on which procedure exactly is done, the price can range anywhere from $5,000-$8,000. This will also vary depending on which surgeon you go to and the area that you are in.
Best regards,
Dr. Speron