Good choice on avoiding the steroid cream, especially around the eye. Unfortunately, what is on the skin is in the blood in about 30 seconds. I can email a toxic 12 list of ingredients to look out for. Amazingly, my kid's shampoo had 6 out of the 12 ingredients and my botanical skin care had 2-6 ingredients in every product.
There are two water systems I'm aware of that can help your body from the inside out. Tap and bottled water have many chemicals and residuals in them. I've seen pictures and have heard testimonials from people who ingested these waters (good for detoxifying and cellular health) and sprayed it on the eczema and had great results. Also, can give you info on a shower filtration system. If she is bathing in tap water, she is absorbing lots of chlorine, etc. Be sure to reduce all sorts of other toxins in your environment too - cleaning products, air pollution, food, supplements, electropollution, etc. Give the body what it needs and it can do amazing things. My website is focused on educating people about improving health by reducing environmental toxins as well as products and technologies that address the issues. livinghealthiernow.com and look under the water tab for some articles I've written. Links to more info on the systems are there as well.
Happy to share any other info with you too.
Take care,
S.