Have you modified your diet? Eczema is a sign that she has food intolerances. Cutting out dairy, lentils and beans really helped us. I also cut out gluten and sugar but it wasn't till I cut out the dairy that we saw improvements so you've got to find what works. I would put her on a probiotic like baby biotic too.
The fact that she's refusing food also says to me that she may be in digestive pain and is aware that food hurts. GAPS diet would be a great diet for her. Perhaps look at putting her on the GAPS baby diet because it starts with very gentle and healing foods.
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