Well without examination,confirmation of a diagnosis is tough but various possibilities are there for your daughter’s symptoms.First is of flat warts.Also called plane juvenile warts,they are benign tumors of the epidermis and usually occur in children. Flat warts are about the size of a pinhead and usually appear on the face, but can also appear on arms, knees, or hands.Other possibility is of 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, certain foods, plants, metals, cosmetics, dust mites etc.
I think that you should get it evaluated from a dermatologist as treatment modalities for both are different.
Hope it helps.Take care and pls do keep me posted in case you have any additional queries.Kind regards.