You know, i just went through a tough break myself and i was with you all up until you said you were 18. believe it or not you and your girlfriend know nothing about yourselves. You're too young to be making a commitment like that in the first place.
I know its hard trying to think outside of yourself but being 18 years old you have to realize that you know nothing. That what you like now you could hate in a couple months. I'm not saying that if you were happy with here you should ends things because you're young. I'm saying don't put such lofty expectations like marriage over a young relationship.
Finally, once someone cheats on you, you have to move on. The relationship will never be the same and its just easier to move on.
If i were you i would try my best to move on and stay away from her for at least a couple months. It sounds like she's doing you a favor and this could have been the best thing to ever happen to you. I bet in 2 years you'll look back on this and kick yourself for even considering trying to win her back.
Edit: oh shit, i just read your update... i was pretty much spot on though.
There's nothing wrong with getting married at 18 if you're sure about the person you're with. Sounds like you weren't though, so you'll get over it. Don't see anything wrong with her getting with someone else after two weeks though. That's actually reasonable. It's not like she went and fucked someone the very next day after you two split. Seriously, how long did you expect her to hold out?
But yeah. You'll get over it eventually. Just don't beat yourself up in the meantime.
You don't get with someone after two weeks of being in a relationship unless it meant absolutely nothing to you or it wasn't serious. That was a really shitty thing of her to do. She's not worth your time if she can just get with someone else that quickly.