Have you by any chance come into contact with the following:
Acrylic Floor "wax"
Any other "lacquer" type substance?
Twice I've had this problem. The first time, it was a reaction to superglue. I spilled it on my hand trying to fix my eyeglass frames (eyeglass frames do NOT take well to superglue, btw) and *thought* I'd gotten it all off with acetone. One morning I woke up with hard shiny bumps all over my hand. I tried poking one with a needle to see if they were blisters - it wasn't. For a couple weeks I was embarassed to shake hands with anyone. Eventually a thin layer of skin peeled off and the bumps went away. My husband was the one who figured out the superglue answer, only because he had a coworker have the same thing happen. It looked like alligator skin, only shiny.
My husband thought the bumps were a result of my skin not being able to "breathe."
I never use superglue anymore, but I had this reaction a second time about a year ago, and this time it was confined to the area around my wedding band. I gave my daughter a fancy "updo" hairstyle - it looked great, but I used a super-strong hairspray from the beauty supply store. I managed to keep it on her hair and off her face and neck, but I evidently got it under my wedding band and it didn't all come off when I washed my hands. As soon as the bumps started, I cleaned with a tea-tree-oil based solvent that will take off paint but is still safe to use. After that I just kept washing with Dr. Bronner's soap. The bumps stayed around for a few days, but the skin didn't peel off.
Moral: If you MUST use superglue, strong hairspray, nail polish, etc. - CLEAN YOUR SKIN WELL AFTERWARD, and take off your rings when you do!
I don't use superglue anymore, only use nail polish to stop runs in panty hose (my kids use it on earring posts and backs, though -they're sensitive to metal and the polish keeps the metal from contacting their skin,) and hair wax works pretty well for styling once you get the hang of it :)