When you say your house is allergen proof, does that mean that your household water system is free of chlorine/fluoride? These chemicals are used to treat water and rid it of harmful bacteria; however, those same chemicals are extremely toxic to the skin. A recent trip to the beach and a severe flareup of my Mother's eczema skin after spending time in a chlorine treated pool, along with overexposure to chlorine in the hotel shower, reminded me of level of eczema irritation that chlorine/fluoride do bring. In most places the water is treated with chlorine/fluoride. In order to remedy that problem, a water purification system attached to your shower heads or bath faucets will take out those toxic chemicals before they make contact with the skin.
In addition, when you say your house is allergen proof, does it mean that there are no household pets (like cats or dogs) in the house. Pet dander is both a major airborne & contact allergen/irritant.
Your child's immune health needs to be restored. This is done through nutritional whole food consumption. The deficiencies that eczema represent are: beta carotene, zinc, quercetin, essential fatty acids (omega-3, omega-6, omega-9 & GLA), vitamin C, vitamin D, & vitamin E. Have any of the doctors ever mentioned or even addressed these particular deficiencies with you? And also, what foods/drink does your daughter consume? Also, keep in mind that when a child is given allergy tests under the influence of an immune system being suppressed by medications, then it is highly likely that a child or individual would show allergic reactions to mostly everything since there is no resistance (shut down immune system). I say this to say that although it seems that your child has a future filled with pain, this does not have to be the case. Her immune system is sick right now; but that, indeed, can change. Not by medications; but rather, by your attention to feeding the body the nutrients needed to restore the immune health.