I'm in the same boat. I don't wash my face, just use water, because any cleanser makes me so so so itchy. The only makeup I wear is a little tinted Nivea-brand chapstick. Everything else makes my face feel like it's got a mask of itch on.
Been using Kiehls eye cream, which hasn't been irritating me. I don't use facial moisturizer at all, but usually after I finish using some CVS-brand vitamin E cream on my legs, etc, I'll pat my face with my hands. Seems to give me a little moisture without too too much reaction. A pharmacist in India once gave me an incredibly inexpensive tube of a vitamin E cream for my face. It was the most comfortable lotion I'd ever used. I wish like anything I'd written down the name...and bought 100 more tubes...
I went to a dermatologist in DC who said that I could use cortisone lotion on my face. I'd been told before not to do that. Have done it a little; hasn't seemed to help. She also gave me some other special lotion that's for extra-sensitive skin and it made me go crazy with itchiness after a few seconds. So, yeah.
I've been to Nusta spa for facials with Rebecca. She's done magical things to my skin. I walk away from sessions with her feeling a gazillion times more comfortable. Highly recommended. (She's given me samples to use afterwards. Invariably, they end up making me itchy.)
Looking forward to hearing other people's favorite brands, doctors, etc.