Greetings. You seem to have allergic contact dermatitis. But I wouldn't say that this is due to
vitamin deficiency. However contact with soaps and detergents worsens hand eczema and you must minimize contact with the same, and use gloves instead while doing house hold chores. Use Vaseline jelly time and again to keep hands moist. Hope this helps. Warm regards
Next Steps
see a qualified dermatologist near you