I'm also in the process of trying to decide who my letter writers are, so take my advice with a grain of salt. If you have some professors in mind who you think have a good opinion of you, but don't know you well enough to write a superb recommendation, I suggest that you find time each week to attend their office hours. They already think you are intelligent and hardworking, if you get to know them more and share with them your future plans in medicine and your motivations, they could likely write you a fantastic recommendation!
I've heard it said before that when asking for a letter you should give the letter writer ~ 4 - 6 weeks. Using that timeframe, you have until late April or early May at the latest to ask your professors. See what you can accomplish in that time. Good luck!