I use pure vegetable glycerin as a body lotion with good results, and I have severe skin sensitivities. If you want a more mainstream product, try Lubriderm Sensitive Skin
formula (the aqua label). It's lanolin free, too. If you're allergic to wool, you should avoid lanolin. Shampoos, lotions, deodorants, etc., should have no ADDED fragrance, which includes masking fragrance.