Hello,
For eczema,wash the areas several times with fresh water. Do not use any cosmetic products at the sites. You can apply some calamine lotion at the rash as it will help in soothing the skin.
For mild-moderate eczema a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide) but seeing the age it is advisable to use mild steroids.
Eczema can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
If still the symptoms do not improve then pls get a clinical examination done by a dermatologist.
Hope it helps.Take care and pls do keep me posted on how you are doing or if you have any additional doubts.Kind regards.
Quite safe to use hydrocortione creme during flareup but return to zinc creme in a week or so.