This drying of fingers can be due to eczema. It is a form of chronic dermatitis (rash).Allergic reaction is one of the important causes of eczema. Allergic reaction can occur to strong soaps, Solvents, chemicals, certain foods, food additives, plants, metals, cosmetics, even urine and faeces of some animals (dust mites).
I would suggest you to consult a dermatologist and get this possibility evaluated. Treatment depends on the confirmation of diagnosis.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.
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