My initial feeling is that this anxiety could be caused by being out of control What about you being in control on setting the limits. For instance.

Have your partner sit on one end of the couch and you on the other. then at your command your partner and you will only move a specified amount and not do anything you don't authorize. This is an exercise to try, not a pattern for your relationship.

When you reach a point where your anxiety starts to come up, see if you can identify what it is or just get in touch with your breathing. When you get within arm reach, you could say okay let's hold hands.

This is not a very spontaneous way to relate but as an exercise it can help diminish or get you to feel comfortable with a certain amount of anxiety.

A therapist could help. There might be medicines to diminish anxiety.

Here are some articles that might be of interest.
Psych Central - Search results for Hypersensitivity to touch