I have an overbite from sucking my thumb. I've stopped doing since last year, and now I am 18. So, at age 17 I stopped. Embarrassing, but it was extremely addictive

. I want this overbite fixed. My teeth are really straight, it's just this little overbite that I don't like... and at times, refrains me from smiling much.
Can braces really fix an ex-thumb sucker's overbite?
I am planning to get them on, a little after my 19th b-day, which is in early Jan.
Any advice, I'll appreciate!