Hi,
Welcome to the forum and thanks for posting on it. 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. You can take some OTC oral antihistamine medications like Benadryl or Claritin and see if it helps.
For mild-moderate eczema a weak steroid may be used whilst more severe cases require a higher-potency steroid.
Eczema can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
If the symptoms persist then get an evaluation done by a dermatologist. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care.