This one had me stumped from what I had read and thought I knew about Virginia Creeper. I pull the stuff up by the handfuls and never have an issue. I didn't doubt that you were having an allergic reaction but I'd never come across any information about it - until now that is. Check out this link -
http://www.calpoison.org/public/plants-toxic.html
which is the California Poison Control System. There listed for Virginia Creeper is the sap can cause a skin rash or irritation. Apparently, the sap contains oxalate crystals which is an irritant.
In order to find this website I had to go through a few dozen others which assured us that virginia Creeper was harmless. Then I found that Virginia Creeper is actually toxic to animals (there are many exotic bird sites which mention this). That was enough information to make me dig deeper and there it was. So no mutant creeper for you - just something that you are sensitive to where many others are not.