OP, I think it's great that you're interested in medicine despite the roadblocks that are out of your control. I personally have a mild form of ADHD (diagnosed as a child, went off the pills quickly when they made feel frustrated). I've noticed the biggest difficulties I have had are also picking up on subtle social cues and forgetting small things like a lunch box at school. When it comes to your profession though, you will be expected to function at 100% for the good of your patients and colleagues. My biggest weapon for combatting my weakness was vigorous introspection and observation skills.
I'm not expert on the matter but here are my beliefs. I define your problem as the inability to learn skills (social) by the means in which others learn them. That's it. So what you need to do is have a hard look in the mirror and understand about what those skills are and how you can start learning them in whatever way you can. Mild ADHD =/= Aspergers Syndrome but let me share with you some I've tried over the years to improve myself that have led to success.
I think some other posters hit the nail on the head when they said quiet vs talkative is rarely the problem, but perceptive vs. lack of perceptiveness is. As a child, I started out "introverted" but tried being an "extrovert"...but then my friends kept telling me I was being rude/missing things in conversations. Over time, I quieted down and learnt to listen as opposed to focusing on what I had to say. This made it easier for me to pick up on cues and now rarely do I have the problem of missing social cues. Also, another thing I tried was just sitting quietly and watching how others acted. What I noticed was it wasn't what peoples said that was as important but how they said it.
As a result, I found myself better able to perform and be professional while being a quieter person. I also happen to enjoy spending most my free time alone learning new skills or socializing with 1-2 people. If that gives me the label of introvert, so be it. I just do what works for me. The introvert/extrovert schism isn't even real, but was written about by a self declared psychologist who came to his views as a result of surmisation and introspection. After that, the labels stuck because people love to feel special and part of a group. Oh! I'm an INTJ, of course I can take a bunch of details and synthesize a deeper meaning or oh, I'm an ESFP...I'm great in clutch situations.
OP, I do believe that an Asperger's individual can be an exceptional physician but there may be more work involved in becoming one. In the meantime, don't become bogged down with all these stupid labels. Just be humble, recognize you have flaws that will make it more difficult for you, work hard, and do what works for you. That's the way you can be succesful.