How can I heal my childs eczema on her face?

Eczema on face. Try to identify the triggers, and eliminate them. Some common triggers are soaps, detergents, milk and eggs. In general, topical steroids are not recommended on the face, but if the eczema is very bad, you could apply a very thin layer of Hydrocortisone 0.5%. It's always prudent to take your child to a pediatrician.
Control not cure. Usually means your child has sensitive skin and there is not one thing causing it. Avoid irritants, moisturize and seek medical care if the eczema persists.