consider how much your face impacts your quality of life, socially, professionally, mentally - that it to say, out of everything you can do in this world, nothing will have a more dramatic impact on every aspect of your life than your face. This applies both ways - good and bad outcomes.
I think it is definitely worth it in your case and although its only a profile picture and not a front on one, I think you will be quite attractive after the surgery is over and you are fulled healed.
Also, you if you're worried about committing to the braces period, you could get a second opinion from a doctor that performs a "surgery first" method. I'm not sure if you'd be a candidate for it, but considering you say your teeth are very straight, I think you probably would be.