My friend had surgery to correct her jaw before she came to uni. Her bottom jaw was further forward than her top jaw (can't remember if that's an overbite or an underbite...) The procedure was all done and everything in the summer holidays, and by the time I actually met her I would never have known. She was still wearing braces but that was for her teeth not her jaw. She said it was fine except she felt a bit miserable while she was in hospital cos she could only have liquids as her jaw was wired shut.
I used to have a bottom jaw that was far too far backwards, but I didn't have surgery for it. First I had braces to straighten my teeth, then I had a different kind of brace which fastened to the top of my mouth but had a sort of plastic trough thing sticking down that my botton teeth had to go in. This meant my bottom jaw was made to stay further forward than it naturally was, and after a few months it stayed like that permanently. It looked a bit like I was wearing a mouth guard like I was going to play rugby or something, and at times it was a bit uncomfortable having my jaw pulled forward like that (I got headaches at my temples sometimes) but I was glad I didn't have to have surgery, like I would have done if my jaw was too far forward instead.
I don't know if that wouldn't work for you because you're older than I was or your jaw is just too far back, but definitely have the surgery. When it comes to getting your teeth and jaws sorted, it makes an incredible difference in the way you look when they are.
Good luck :-)