I had eczema where you describe and was told for decades that it was NOT food related. As a 40 something adult, I now know that it IS food related -- for me, wheat, milk and the nightshade family (potatoes, tomatoes, peppers, eggplant, tobacco). Those were foods I craved.
Has she had a recent vaccination or antibiotics that could have triggered an immune reaction?
You can try removing any food that she craves for four or five days. Ask the doctor about essential fatty acids (fish oil) (get dosage info from the doc, too). That helps me, but I am just a mom, not a doc, and this is not medical advice.