A way out or at least your opinion

Hello everyone

I've been a long time lurker and I wanted to join and see what you guys think or my circumstances.

First, I know the forum is about management consulting, so if this annoys you and you don't want to respond doesn't hurt my feelings I understand.

I have been out of school for a couple years now from a non target, graduated in the midst of the crap storm, ended up at a hospital working with Epic. Have done it for the past couple years, moved into a role as a team lead of a small team and now am at a uber prestigious research hospital as a consultant (think Johns Hopkins, Cleveland Clinic, Mayo Clinic). I'm no longer someone who is just stuck behind a desk doing the IT part, I go out support and meet with the business side, do presentations in from of the board and such, but there is a bit of IT crap.

Here are my questions...

Does my current hospital help my resume for bschool? A lot of the schools I have looked at have hospitals under their cloud which use epic and I might be able to get into one of them. Does working for a top schools hospital like University of Chicago help chances of getting in their business school?

Are there any exit opportunities that could come out of a position like I am in now at a good hospital?

Should I be ready to jump for a hospital that has a good business school if I got an offer?

I really don't want to stay in consulting even if it is management, I'd like to go IB or PE.

Thanks in advance!