Not all cases of eczema are allergic in origin but a lot are. In that case it makes sense to eliminate the allergen rather than add medication.

The two basic kinds of allergic eczema are the ones caused by food allergy and the ones caused by contact with environmental allergens. The difference is the site. Food allergy eczema is usually on the INNER surface of the knees, groin or elbows (areas that won't come in contact with stuff like floor polish, shampoo or whatever). Whereas eczema on the CONVEX surfaces of the body is usually because you're rubbing against an irritant.

Commonest eczema-causing food allergens: dairy products, eggs, wheat, nightshade-family plants (tomato, potato, tobacco etc)

Commonest environmental allergens: perfumes used in scented products, with household cleaners, detergents, deodorants and fabric conditioners being the worst. ESPECIALLY fabric conditioners - they're evil shit and nobody should use them (there are no scent-free ones).