Having trouble responding to professors' emails due to anxiety,
You are doing the right thing seeking some medical advice. But the way to become more comfortable in this, as in most things, is:

Practice. Practice. Practice. 

The first steps are painful and you may fall. Eventually you learn to walk and probably to run. 

My doctoral program took a few years longer than it might have because I was too afraid to speak up on my own behalf at a certain point and got stuck (really stuck) with an unhelpful advisor. 

Later, I took on the issue head on and taught myself to look people in the eye and to speak up. It was very difficult at first. Now I do it without thought or worry. 

It is just a skill. Learn to apply it. Haltingly at first, but it is extremely unlikely that bad things will happen if you speak up. If people don't know your needs they will not be able to assist your academic growth. Just. Do. It. Grow into the person you want to be. 

Sometimes you need to just pretend to be the person you want to be.