If you're feeding breastmilk, it could be the food which you take that causes the flare up. Do see a PD to determine the cause of the eczema.
What you can do for your baby is also to embark on an elimination diet. Baby may be sensitive to milk, gluten, peanuts, etc. http://kellymom.com/health/baby-health/food-sensitivity/
As for the exterior, do keep the area dry and free from soap. The California Baby Calendula cream has worked for many mums to keep eczema under control.
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