Hello,
I can understand your concern but from the symptoms definitely eczema is an important possibility as it often presents with red, itchy, dry, flaky skin. 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 suggest you to get it examined from a dermatologist to confirm the diagnosis.