I sympathize with you. A person wants to take care of "telling people" himself, not wonder if someone you don't know is going to take care of it for you. Will she be discreet, or is she the type to spread gossip like the flu? She might have the best intentions but still misunderstand - maybe she thinks you're "out" or at some moment of"sharing" with her cousin (or a someone she meets from your school) decide to "share" your business.
Maybe you've been thinking you'd like to just get through High School before coming out, get that petty world behind you and into college before telling your friends and parents ... to be able to tell them your way, one at a time, etc.
I get that. On the other hand, I've had friend "outed" to their parents in similar ways: one friend's sister was told he was gay by someone who was told by another guy who ran into him at a bar ... (so typical). She confronted him and was pretty hostile. THEN she told his mother, who freaked out , of course. But this all turned out for the better, the cat was out of the bag and everyone eventually dealt with it.
However, he was in his late 20s, out of law school. Not 18, living at home, dealing with the cliques and other issues of high school. So I can really appreciate the difference for you.
You have a few options immediately open to you -
1. You can find out who this girl is, in fact; is she really your best friend's cousin? You could then follow up with her, since you've met now, and privately tell her you're not out (possibly not even 'decided') and ask her to keep it to herself. Maybe you should ask the guy who was the original contact about her ... get your facts straight and find out how much you have to worry about.
2. You can ride it and see what happens. Maybe nothing.
3. You can privately tell your best friend what's up before she does. You can even leave out the part about her, just tell him you're gay. Or tell him you "might be" gay, if you want to break it easy. (I had that conversation with a couple of friends when I was about your age - because in fact, I wasn't sure. I knew I liked guys, but thought then that I would probably enjoy that then later "move on" to girls and getting married. In none of those cases did the friend freak out or even alter their relationship with me. But many people have different experiences.)
You're smart to post your dilemma here. There are as many different experiences of "coming out" and being "outed" as there are guys here.
In my case, a few months before I finally came to the realization that it was to be men only for me, and no wife somewhere down the line (I was dating a girl, who was pretty frustrated that she couldn't get me into bed!) I met a guy and brought him home. He knew lots of people I knew, and the very next day I was hearing from one of them how cool it was that he and I had hooked up, she thought we were perfect for each other, etc. YOW! I felt ambushed.
It turned out to be just another step for me, and didn't have any actual repercussions at all. (Except that it made me distrust him just enough that we never slept together again - and we actually might have been pretty good together.)
So, final advice for now: keep calm. Don't freak out. You sound pretty well sorted, so fall back on your ability to keep your cool.
Watch the booze. You can do far worse damage to your reputation and future getting drunk and losing control of your actions than you can by experiencing an outing by a high school girl.