Having surgery is an incredibly personal decision; it's something that only you can decide is right for you or not. I've had 5 surgeries in as many years, and I eventually quit telling people I was having surgery. My last surgery was a "two-week vacation" so that I didn't have to take sick leave and tell anyone what was going on.
In addition to having had multiple surgeries, I've lost a lot of weight - more than 100 pounds. Losing weight has been the best thing I've ever done for myself, for so for many reasons. When I was heavier (and I'm no skinny girl now - I'm a solid size 12 and I can't wear button-down shirts), my back, knees, ankles, and feet always hurt. There were days when the back pain alone made it physically impossible to get out of the bed. No one needed to tell me that losing weight would make me feel better (and make the boobs a little smaller)...but I can't express just how much better I feel in every aspect now. Living with chronic pain is no way to live. You are young enough to take action now so that you don't have to spend an entire lifetime dealing with the ill-effects of being overweight.
Personally, I think physical therapy is great first step towards getting well. And I agree that water exercise is a great place to start. I'm sure your PT will be able to recommend things you can do to become more active without aggravating your back and other issues.
And yes, invest in a great sports bra. I nearly gave up running and riding because it hurt the twin peaks. I've spent a small fortune on finding what works best for me, but it's been worth it. I can now ride/run/skip/dance in comfort! I always wash them on the hand-wash cycle, with gentle detergent, and I never, ever use fabric softener on them, nor do I put them in the dryer.
Best of luck to you!