Every boarding school has a group of the overconfident, know-it-all, master of the universe kids, and the top boarding schools certainly get a fair share, and I don’t get the impression they shy away from them at all. So as long as OP can reign it in during interviews, she is likely fine. Bragging in the essays is expected and even encouraged, assuming it can be back up by actual accomplishments. Besides, she is 14 and I bet a lot of what we see here is just her Internet persona.