Your baby's sweating is probably normal. Her other problem is not normal. She must have lactose intolerance or a milk allergy.Her illness sounds like a condition called eosinophilic gastroenteropathy which is a form of milk allergy [look it up on Google]. Try her on a special formula called Neocate just to see if she improves rapidly. This formula is very expensive but some medical aids will pay for it.Let me know what happens when you change your baby to the Neocate. You must not give her any solid food which contains milk eg Cerelac or yoghurt.
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