Thank you for the advice! At work we have three sinks in which we sanitize the dishes. I think this mat be the cause to my hand irritation.
Just in case it's dermatitis, the only advice I can give you is to avoid water, especially if it has detergent in it. Wear protective gloves and don't expose your hands to sudden changes of temperature. If it gets worse, go see a doctor. By the way, dermatitis is treated with topical corticosteroids. Don't take antibiotics if you don't need them.