Dressing professionally means no jeans or khakis, T's or casual shirts. Dress slacks, dress shirt, tie and jacket. A suit is definitely okay, but I wouldn't say necessary in this case. For a med school interview though, I'd suggest a suit. Make sure your shoes are also appropriate to wear with your dress clothes. A friend who just shadowed recently was advised by the Dr. to "dress professionally, wear a jacket". She was surprised since she thought dress slacks or skirt and a nice blouse or sweater was appropriate. She followed the Dr.'s suggestion and he did comment on how appropriately dressed she was. She was shadowing in his office and then checking on hospital patients. A lot of Dr.'s want you dressing in the same manner they will be for whatever the work situation is. I agree with the previous post, it is always okay to check with their office if you have any question on attire. Have fun shadowing and good luck.