We went to big London hospital recently, and their best practice on eczema:
Use an emollient thick enough to write your name in. Apply in the direction of hair growth, in strokes, do not rub. Leave until sunken in, up to 20 minutes. Then apply a thin layer of the steroid. Do not scrimp on it. As a pp has said, a steroid is not great for skin, but eczema is fr far worse.
With creams in pots, use a spatula or spoon to get cream out, not your hands, as you do not want to contaminate the cream.
Apply the moisturiser every nappy change if the skin looks dry. Keeps using for a few days while there are no symptoms.
Hydromol ointment is good if it is very bad. For light moisturiser, we recommend Aveeno cream (oats are active ingredient), and Lush Dream Cream (essential oils).
Do not put anything in the bath water, though you can try a sock full of porridge oats (tied up) which you can squeeze.
If you are offered allergy testing, do have it. DS's skin is transformed now