I get really bad eczema on my hands, particularly on my right hand. I can't touch cleaning products, hand soap, nothing. :L I'm also asthmatic, and have horrendous allergies.
I adore Longhaired hammies, but I've realised I'm really allergic to them. All I have to do is give Tansy or Jack a quick snuggle, and my hands itch and crack, my throat starts itching, I sneeze and my eyes start streaming... But it doesn't stop me haha.
For my hands I use something called Dermol.
You can get it at the chemist. Its brilliant stuff. Its a moisturiser that is also anti-microbial, so you can use it to wash your hands instead of soap. As I can't use soap on my hands, it's ideal (even things like Simple make my hands flare and itch so bad they bleed). Only thing that has ever worked for me, and my hands have had everything from E45 to steroids. :L