Quoting A, E & W's mommy:" and she had literally not slept at all? or has she slept in spurts? what are you using on her eczema? ... [snip!] ... would be if the eczema is triggered by an allergy and if that allergy is finally getting the best of her insides as well."
I was just about to recommend several of the things you mentioned! Also OP, hazelwood necklaces are supposed to help tremendously with eczema. With my kids we used phisoderm baby bath and then any lotion without alcohol. Paying attention to ingredients is VERY key, many "eczema" lotions contain alcohol, which is counterproductive since alcohol dries you out. Also, all of my kids were sensitive to dairy. My son in fact was the worst. He had no hair except a strip down the middle. Our pediatrician called him alligator head
A week after we switched his formula to a non dairy based, he had little stubbles of hair growing.