Do you ever feel ashamed when meeting someone "better" than you?

I’ve been taking a summer class at the local community college. There’s a girl there, another student in my class, whom I’m attracted to. The thing is, I found out the other day that she came from a private, very exclusive high school in the area, isn’t even a freshman yet (just taking the class to get ahead) whereas I’m already a junior at a mediocre state university, and… she’s going to Georgetown Uni in the fall (private, prestigious, and clear across the country).

Needless to say, ever since I found out, I’ve been feeling inadequate. Just… ashamed and very intimidated. I could laugh at myself (in fact, I’ve already done so several times) for even thinking I’d have a chance with this girl.

Has anyone else experienced something like this? At first I was kind of angry at her… because, I don’t know, I wanted her to be on my level (stupid, stupid reason) but now I’m just feeling bad for myself.