Will My Insurance Cover Breast Reduction?

I am 20 years old with 36DD breasts. I am a healthy weight, and I have heard many stories of women with much larger breasts, but I have a small frame. My breasts cause bad posture, and strain in my neck, shoulders and back. Although I am at a healthy weight now, diabetes runs very strongly in my family, and I am worried about how I will exercise (aside from eating well) to avoid this disease. It can also be emotionally trying. On the lighter side, I don't have much spare money and most of the bras I can find that fit are ultra expensive..not to mentions it's hard finding tops and affordable bathing suits. My insurance is Oxford but we are switching it, and it might be switched over to Blue Cross by the time I get the surgery.