I'm obviously sorry for what you've been through and are going through.
There are many issues with respect to insurance. Each insurance company is different, and each has its own rules with respect to "coverage." You'll first have to contact your company to make sure it's covered, and then you have to find a surgeon who will accept the payment the insurance company says is "usual and customary." That may or may not be easy to do. If you start with the surgeons who participate in the insurance company you'll be off to a good start. If you'd rather use a different surgeon, and you have out-of-network benefits, you can contact the surgeon's office and see if he/she will accept that payment.
Either way, you'll need the help of a plastic surgeon to submit a letter of precertification (typically including your height, weight, bra size, specifics of any pain that you have and how your enlarged breasts affect your health and quality of life) and photos and to make sure that everything is set before you have the surgery. In your case, having the history of back problems may be helpful in obtaining insurance company coverage, but you will still most likely need to have enough tissue removed for them to consider it and, based on your size, you may or may not then be happy with the final result. You should, of course, meet with a few plastic surgeons to see what they recommend, and make sure you're informed about the procedure and its risks so that you can proceed knowledgeably. If you do all of this you'll be most likely to have a result you'll be happy and comfortable with.
The insurance company may also ask you to lose weight and/or try conservative therapy before making a determination. In general, they are less likely to provide coverage if it's a question of correcting asymmetry; and more likely to the extent that the surgery can provide symptomatic relief of some kind.
I hope that this helps, and good luck,