Hi Elena!
I recognise not wanting to talk to friends/family as the reactions you get (possibly because you are a woman) are usually not that great. You should have seen the look of horror on my mother's face when I told her....
I'm going over to the US in October and the TSA stuff wasn't too tricky to get through, took about a week, although I'm Swedish and it might be different. You have an advantage in that since you're young you probably don't have a gazillion addresses, previous names/marriages like some of us...
Picking a school is always difficult, I think sound advice I've gotten is make sure you can leave if you don't like it, there are many others.
Bon chance!