My husband has only one hand with severe dry cracked skin and nails are dry and fungal?

Contact dermatitis? If he is using that hand for routine work and coming in contact with something he is allergic to he can get skin inflammtion and irritation. Try to avoid direct contact with some thing that is irritant, e.g. If detergent than wear Gloves, If gloves are the culprit than use Latex free glove. Try OTC Hydrocortisone cream fo 3 days. If not better or getting worse, please see your doctor for propei.
Possibly. Get this checked by a GP or dermatologist.