If you're 15 and your mom doesn't let you go out or let you see girls then I'd say you have even bigger problems than this girl (who sounds terrible anyway)
Also as somebody who made the transition from dorkwad to less of a dorkwad to eventually pretty cool, let me kick something down to you; you need to do the same thing and then you'll get more girls in general
Start making cool friends. Can't actually remember quite how I did. It just kind of happened. But do it. Also, consider what you're bringing to the table that makes you worth this girl's time. Even if she likes you initially that's not enough; you have to be worth her while. Remember they're the sex that does the selecting. If you want to bang 'em you have to give them what they want. So what do you have? Cool friends, interesting talents and hobbies (DWARF FORTRESS DOES NOT COUNT! except negatively. There's no way in hell I'd tell some girl I did stuff like playing Dwarf Fortress or Magic the Gathering until I already knew her pretty well. Girls smell that shit and run like hell), and good social skills - namely, (and science has begun investigating this) you're nice to her and her friends and dominant toward other guys. Dominant meaning you're comfortable, you don't need to put other people down (that makes you look insecure) and you are able to hold your own in the competitive world of being a dude. You don't take shit.
There's your homework assignment young padawan now let me see you get some ass!
There is so much wrong in this post I don't know where to start.
1) Sex isn't (or
shouldn't be) the only reason you're interested in girls.
2) We shouldn't be assuming that they're going to have sex on the first date anyways, especially since they're 15.
3) If you need "cool friends" to get a girl, she's not worth your time. If she doesn't like you for who you are, you should just forget it. Of course you need to move away from the dork-zoid zone, but you should
never try to be someone who you aren't for a girl. If you do, it ends badly.
4) If she likes you for your "cool friends," that should be ringing alarm bells all over the place.