It really depends on your insurance companies criteria for covering jaw surgery. In general insurance companies won't want to cover this, they are in it to make money not for charity, and the exclusionary criteria has changed for a lot of insurance companies since ACA has taken effect making it harder to get this surgery covered. I wish there was one thing I could tell you to do or to try, but it really depends on the fine print of your specific policy, some will outright deny it regardless of proven necessity, some will cover only if it is proven medically necessary, a small few might cover it with no questions asked but from everything I've seen, those have gone away in the past 2 years.
If you have a narrowed airway, sleep apnea, or a large malocclusion that cannot be corrected by braces alone that will improve your odds of getting it covered.
Edit, I just re-read, did your insurance per-approve for jaw surgery but not braces? Most insurance companies won't cover for braces as that falls under dental not medical.
