OP, I’m going to take the opposite side of everyone else in this thread. You felt you clicked with Caltech. You have the grades and scores to be a plausible applicant, per your post, if not quite the optimal rigor. They have a major you want. Why not apply?
By all means look into CMU, MIT, etc. But don’t let a bunch of people on the Internet dissuade you from applying to your most desired school. The worst that can happen is you get rejected.
EDIT: old thread.