One of the causes of infantile eczema is lack of the right fats in the diet, such as omega 3. When my 5 year old was an infant, she had severe eczema due to malnutrition. I tried a lot of ointments and creams, but it didn't clear up until I started adding flax oil to her bottles. Since your baby is being breast-fed, you might want to add an oil supplement to your diet. One of my favorites is Barleans Essential Woman. More often than not, what we see on the outside is actually a symptom of what is going on on the inside.