You're not going to be out of your league. When you get to Northwestern (if you come! Which you should!) you're going to meet a lot of people who come from wealthy backgrounds, have connected families, and went to impressive private high schools. That's just the truth of it, and if you come from a background that's not like that, you might be a little intimidated at first. I felt that way when I first got to NU -- I was like, "Holy crap, how am I supposed to compete with these people?"
But the truth of it is that everyone is at the same school, everyone is taking the same classes, and everyone is capable of doing well in them. And anyone anywhere who tries to feel superior to or intimidate other people by seeming smarter or more powerful than them is the one who's lacking something. But those people aren't common at Northwestern anyway -- I feel like Northwestern is a pretty humble, friendly, and welcoming school overall. I really love it here, and I am by no means a competitive person.
Basically, try not to worry about this sort of thing too much. Assuming you do the basics, like go to class and doing your problem sets, you'll do fine in your classes.
As Regina Spektor says, "People are just people. They shouldn't make you nervous."
Good luck choosing where to go.
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