I don't think advice that basically boils down to "look on the bright side" is helpful.
You're allowed to feel disappointed and hurt. That's okay. You've experienced a kind of rejection, and it probably fuels feelings of inadequacy or unworthiness. Maybe it echos things you used to hear about yourself in childhood. I don't know.
The point is that everyone has experienced exactly what you're feeling right now. And I promise it's going to happen to you again. Just like it does to everyone else. I wouldn't personalise it (there are many reasons why people are awarded scholarships and exactly none of it has to do with what you're worth as a human being), and I would focus on all the great things about yourself that got you into medical school in the first place.
Another approach: let yourself grieve and use it as fuel. You got a chip on your shoulder? Cool. **** em and prove them all wrong. Hell yeah.