Irritant! I thought this post was about Graham Ghoul.
Ahem. Yes, some people, like myself have skin that is intolerant to detergent. I would say I've 'sensitive skin', but because I'm a Geordie, I don't want to sound soft!
Just prior to Christmas my hands were really badly cracked, extremely dry and almost stopped me from working. See your GP. They'll issue you with a high-content hydroquorasone cream (but probably spelt a bit differently) and a good quality emolument cream.
Then, use rubber gloves (you can get them from any hardware shop - buy Xtra Large) and cotton inners (you get these from boots). Buy three or four pairs of inners, because when your hands sweat, they get wet. Just keep on changing them for a dry pair.
It takes a little getting used to, but now I feel strange cleaning without them.
Oh, I've also got suntanned arms and white hands. But my hands are in good nick!