my eldest girl also had eczema and dry skin since birth. what matters most is to keep the skin moisturised all the time. For my girl, it was so bad that if she perspires, she'll break out in rash. I used pureen yoghurt body wash.
When there is still rash, you need to treat it first. I got the cream from my pediatrician but bear in mind that these creams contains steroid so not good to use a lot or for a long period of time. Once she's not scratching, I'll put moisturiser on her. 2-3 times a day. I used QV kids moisturising lotion and I must say that it is very good. Even my pediatrician said that it is good.
I was worried when my girl entered childcare as I felt bad asking the teacher to put moisturiser for her many times a day. Thankfully, she rarely has breakouts now (I can't remember when was the last time she was scratching). Now, I only put moisturiser for her once a day.