You need to wash the areas several times with fresh water. Do not use any cosmetic products at the sites.
Apply calamine lotion at the site of the lesions and see if it helps. You could take some oral antihistamine medications like cetrizine or loratadine. You need to maintain a good personal hygiene .
Anti-itch drugs, often antihistamine, may reduce the itch during a flare up of eczema, and the reduced scratching in turn reduces damage and irritation to the skin.
You could consult a skin specialist if your symptoms do not resolve with the above methods.