I'd say when asking for feedback, the humble willingness to learn, no matter how the feedback is delivered, or by whom the feedback is delivered, is the key to success. Often when we find ourselves at this stage in any process it's likely because there is some great "elusive obvious" that we can't see for ourselves, but is actually right in front of our face.
If someone asks for and receives lots of feedback, however, and doesn't appear willing to hear the message all around them, then stop giving feedback, okay? Anybody remember Rocky, the movie? When his crusty trainer made him chase all those chickens in the alley? I think chasing chickens can be a pretty frustrating experience. Let it go. Life keeps giving feedback with or without your participation and it's up us when we are fully open to it.
By playing Villian to somebody else's persona, you just help keep their problems going. You provide them with the very thing that they need to push against. And in addition, you have given yourself the feedback that there is something at stake for you in the very game that you are giving feedback about. That is, you might want to examine why this is such a hot button for you (What's the pay-off for YOU). It's funny to think that if a certain approach doesn't work to solve a given problem, that you can solve it by doing it more, or harder. How about trying a different approach??
Furthermore, it's common to tie one's worthiness as a human being into processes like medical school admissions. When you don't get it in, you immediately jump to the conclusion that something's got to be wrong with you, or the entity who rejected you. There's a sense of blame and defensiveness, instead of authentic wonder. Anyway, for what it's worth.
Best of luck, OP. Keep persisting if med is what you want to do. There are certain elements in the process that are out of your control. No matter what your stats are, or what awesome things you might have accomplished, you are much more than those things. Be humble; there's always somebody who has done more. Rejection or a delay in the process, doesn't automatically equate to something being wrong with you. As I've heard it said, from this thread, in fact, that it's still early in the game. Be open to learning, patient, listen to all the feedback given to you (not necessarily at face value, but what useful stuff you can glean from it), and then let go.