Quite right, Guessed!
I'm in the opposite situation -- I started out at a top prep school, chose to go to a less prestigious private university (for personal and financial reasons), and am starting a grad program at a non-prestigious public school (my program's very respected, but not top-10-ish). So I've got "pedigree" issues of my own, and a different perspective on the issue.
I'd just like to say that, in my experience, posh undergrad pedigree means bupkis. Sure, it impresses people and opens doors, and is sometimes accompanied by a rigorous educational experience -- but given the prestige of the program you're entering, you'll have those advantages (and then some, because of course graduate pedigree matters much more!). More importantly, as many people have noted, you obviously got a good undergrad education and are smart and talented enough to have gotten in to your current program. Don't worry about not being able to cut it; you'll do fine. You've already passed the test of worthiness. Considering the stiff competition among applicants, I'd say you're a big fish in a big pond! :-D All you have to do now is work hard, which is apparently what you've been doing for years anyway.
And when people look at you like you've got two heads, just take it as a compliment. A meteoric rise from obscurity to Ivy says a lot more about your abilities than a pristine pedigree.