You may be suffering from hand eczema which is a kind of irritant contact dermatitis due to use of detergents during washing of clothes or utensils. Cracks and thickened skin on palms can also be due to psoriasis. Please avoid detergent for some time. You can call me or do online consult with photos for detailed prescriptions and other instructions to reduce the recurrence.

It looks like you have finger tip eczema. It can be because of some professional hazards. Do one thing use any emollient every day, it will keep your skin moist so it will prevent cracks. Use any mild steroid cream once in a week to prevent itching and recurrence. Review after three weeks.