Yes I think I have experienced this!!- it is usually one of two things, or both...

1) Personally I am introverted which means that sitting down and talking for 45 minutes can be really overstimulating for me. Like you mentioned with the chatting, except with therapy the topics get intense. Also, especially if it's a really serious topic, it can be hard to be going and then just stop all of a sudden. Does your T give you enough time to cool down?

2) Sometimes I get this when some feeling is coming up that is not addressed. Either some discomfort/conflict interpersonally is going on, and I'm not able to address it before leaving, so I feel uncomfortable. Or the topic itself is so sensitive that talking about it makes me feel restless..

I would definitely feel the way you describe-- on edge--keyed up-- when experiencing some ambivalence toward the T. I am usually good at knowing what I am feeling and why, and for me that intense jumping out of the skin/wanting to be harmful feeling comes from not knowing.