Child strips off clothing

I have a three year old daughter who suffers from skin irritation.  Although there are usually no visible signs of rash, she will often strip off her clothing, even when the house is cold.  The problem seems worse in the fall and winter when we have the heating on.  The other day it was so bad that she couldn't even stand for me to touch her.  She also wakes in the night sometimes requesting a glass of water.  These problems are usually accompanied by fatigue and irritability.  I'm not sure if this is part of the same thing but at one point last winter she had a mild rash and at one point this fall she broke into hives.  I took her to the doctor when she had the mild rash and he recommended using mild soaps and creams like Aveeno.  This helped to a certain extent but we are still having a problem.  I'm not sure if this is related but she also has thin, dry hair.  She is otherwise a very bright, happy, and healthy child but I feel terrible that I can't figure out what is bothering her.  On her bad days she will strip off and crouch down by the radiator or request a bath.  She was also colicky as a baby and I think in retrospect it was because her skin was bothering her.  I'm not sure if this is some kind of surface irritant (laundry soap?), a chemical sensitivity, or a food allergy.  Any ideas?