At such a young age, eczema skin
is one such possibility which needs to be ruled out. Eczema 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 etc.
To confirm the diagnosis I suggest you to get it evaluated from a dermatologist.