Yes. So long as you don't generally have a problem talking to people (i.e. you can make eye contact, talk clearly, get your point across etc), you don't have to be a particularly chatty person otherwise. You've mentioned social anxiety, what do you mean by that?
Interviews are nerve-wracking for nearly everyone - the interviewers will know this, and they won't be expecting perfection. In the weeks leading up to the interview you could arrange a few practice interviews with friends/family members to get your confidence up, or practice in front of a mirror.
Also you might be interested to know that many medical schools are now moving away from the traditional panel grilling style of interview and now use MMIs, which are meant to give a more complete picture of the applicant's abilities.