might be a fungal thing...you could pop to the docs or try an OTC athlete’s foot remedy but don’t tell the pharmacist its for your hands....although “athletes hand” is a thing, I had a friend at school who used to get it.
This happened to me about 10 years ago.
I had a taster lesson in Tai Chi at U3A. The instructor said you might experience some tingling in your fingers. The next morning I wake to find all the skin on my fingers had peeled off, I was left with raw skin and quite painful. I went to the doctors and wasn't given some cream. I don't think he believed me though.