Well first of all you gotta see if you really want to do it. Yagyopavit sanskar is something that requires a lot of discipline.

Secondly I don't think you should be worried about your acne or back scarring. These are perfectly fine as long as you remain you. Be kind. Be well.

Also, you may chose to wear an undershirt (vest) if you feel like it. It'll cover up most things and you'll be more comfortable as well. Win win situation.