I don't know if this will help, but I have learned to call that a freeze response. I think it is Peter Levine who talks about that; when the flight or fight response gets activated and you can't do either, you freeze. I experience the same thing you are describing when I freeze.

With that response, T3 and I have decided that she will just be quiet and patient so that the response doesn't get more activated. When I am ready, I can say what I am thinking and we try to track back what the trigger was so that we can address it.

She will sometimes put her foot up against mine. Seems like kind of a weird thing to do, but it often helps. She does that because it is a non-threatening way to touch for almost everyone. Could you ask your T to try that?