4 year old has had persistant diarrhoea but now constipated for past week. cough, sore thigh, blood test shows low iron and mild eosinophilia. causes?

Multiple: Frequently kids with constipation have diarrhea as loose stool works around the area of hard stool. However eosinophilia is connected with parasite infections which can also cause diarrhea. Low iron levels could mean she is loosing blood in her stool a sign of inflammatory bowel disease. It sounds like your provider is doing the work-up. Be sure to continue to follow-up.