I think you're brave for being okay with people criticizing the way you do therapy even though you didn't ask for that. Some would not be okay with this.

"Yelling" means different things to different people. My 16 year old calls it "yelling" when I raise my voice and talk in an animated fashion about something negative he is doing or when I tell him to stop doing something. Doesn't happen very often. But my words are not abusive and I am not loud, I am not tearing him down or cursing or otherwise talking in a manner that does anything but make it clear his behavior is unacceptable or he is to do something very differently. To me screaming is the uncomfortably loud and obviously rant-y tone of voice and using abusive words. Perhaps yelling is more about being in control and not anger-spewing, where screaming and other emotional abuse is frightening (to me) because it feels like it could go off the rails at any time.

I would not consider yelling as emotional abuse. I don't see, without more understanding, how what your therapist is doing is abuse. It might be harsh or the opposite of gentle.

I don't think my own therapy has had this dynamic of parent/child, but I think that you should carry on as is best for you. I remember one incident years ago in my therapy where my T said "no" in a firm voice and it yanked me out of some kind of distress I was in. From the context, which I can't really remember but do remember how I felt, it was fine for him to assert some kind of boundary in session.

There are some ways I have attempted to get my T to collude my negative thinking, to react in ways I want him to to reinforce my bad feelings about myself, to encourage my goofy thinking or wallowing in some exaggerated state of distress. At these times he has acted with clarity and non-reactiveness in much the way a good parent would. That is what resonates with me about what you are saying, that your T is very clear with you about sticking to the path you've agreed to be on. You have a very specific goal for being in shape to return to medical school, and as long as your T is keeping you on this path and assisting you, carry on.