Every decent teacher is delighted when one of his or her students gets into a top school–indeed, they will feel that they share some of the credit for it. Just be a nice person, and this will not be a problem at all.
Will teachers think I’m full of myself for attempting to apply to the Ivy League/other highly select
It’s not just whether you “show off.” It can be other ways attitude comes across. Just try to be aware. If there’s no problem, then there’s no problem.