Hello,
For eczema skin of face, 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 symptoms 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 they are available under prescription and should be taken only after consulting a dermatologist. Symptoms can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
I hope it helps. Take care and regards.
I recommend avoiding make up, if that's what you mean by cosmetics. I suffer from eczema but not on the face. I did find a good resource online for information that I'm sure you will find helpful: http://www.eczemaguide.com/care/mild_cleansers_for_eczema_skin.html
Once you are on that page you will find other answers to common questions. There is a page specifically about moisturizers, too.
There is even a page about bathing versus showering that would be helpful information for anyone with eczema on the body, for example.