I'm not sure how you made it through IM rounds and surgery rotations in medical school without figuring out what shoes are comfortable, but I'm happy to offer suggestions.
FYI I have sort of weird feet (not as bad as my brother, who is totally flat footed and needs orthotic inserts in his shoes, but bad enough). My arches are very low and long and I have a narrow heel with lots of pronation. I couldn't wear regular "B" medium width shoes until high school (needed narrow "A" width before that), and even now only a few brands really fit well without any heel slippage.
For work I alternate between wearing the Dansko clogs that everyone loves and a pair of Keens (the style I like is "Briggs"). It took me a little while to get used to the fact that your heels are designed to slide in and out of the Danskos, but now I love them. I find the Danskos are great for everything except stairs (which you eventually get used to) and while my feet will start to feel a little tired at the end of the day, I have zero low back pain and once I have the shoes off there is no residual ache or soreness. The Keens are a little better if I will be walking more, but I will eventually get some lower back pain if I have to stand in one place for over 3-4 continuously with them (but my feet get less achy/tired).
I use Saucony running shoes to exercise and run errands, but I rarely wore them to the hospital, they just aren't comfortable enough to stand still in for long periods.
I have seen lots of people in the hospital wear Crocs, but I would NOT recommend them. They seemed completely without support when I tried them on and I have seen way too many pictures of Crocs with needles sticking out of the holes (I know we don't work with needles that much, but imagine accidentally dropping formalin or glass slides or something on your feet with all those holes in them) - there is a reason that you are supposed to wear closed toed shoes in the hospital.
In terms of something with a heel, I would advise that you put comfort over style (or a desire to look taller - the Dansko clogs have soles that are as thick as some low heels anyway) and avoid heels altogether unless you know you won't be on your feet very much when you wear them. I do have a pair of Naot heels, which I found at Nordstrom, for those occasions, but they aren't as comfortable as I had hoped they would be for the price. Although, to be fair, I've only worn them once or twice, so they might need to be broken in a bit more.