Relax
You're worrying too much.
These guys at the embassy are trained to spot anomalies. You not having any documents to prove ties to the uk isn't going to be a big deal. They'll have seen plenty of teens go to the USA to study whilst under the support of their parents.
If you are honest, be yourself and are genuinely going to go to the USA for flight training they'll know and won't stand in your way.
I've done the process myself, and it's pretty painless apart from forking out a few hundred USD for the visa and appointment, oh and being without a mobile phone for the day's outing.