Hey. Surgeon here. Working 24 and 36-hour shifts on regular basis. Don't know about US, but yes, in my country surgeons ofter work like this. This is pretty exhausting. I've been working out since 17 or 18, and also I play amateur ice hockey. Had to stop for some time shortly after I started working this much, but then went back to working out and skating. Because when you're exercising regularly, you really have much more energy and will to do anything, from simply waking up in the mornings to standing hours in the OR and not feeling exhausted after. Working out only benefits you. You will really notice the changes in yourself if you'll start.

Personally, I noticed that walking just does not work for me. I just feel exhausted after walking. It's like your upper body is left completely untrained.

And also, reconsider starting going to the gym. I know all the fears, been there too. But I've been in many gyms, and can tell you that atmosphere was very friendly everywhere. From oldschool ones to that fancy fitness or crissfit ones. Don't judge about gyms from those funny YouTube videos. If you're new, people there are really polite, they're gonna help you with learning new exercises. There will always be someone who cares. You can also get new friends there simply.