Severe burning palms

I get a terrible burning sensation in the palms of my hands a few hours after I have cleaned and filleted several ocean fish. Doing this with one fish does not seem to affect me but any more and the burning is almost unbearable.
I do have an allergy to crustaceans which if eaten swells my throat and generally don't feel well, but I can eat fish with no problem. It only happens if I have been handling the flesh (cleaning & filleting) after a day out on the ocean. Several days after this happens my entire palm will peel.
I have no idea why this happens and would like to stop it.
Can you help me to understand what this is?