Hi there - My daughter has had eczema since she was 2 months oldT. I had a natural childbirth and she is exclusively breastfed as well. She is doing much better now and I want to share some things that have helped us.
1)Diet - sounds like you are doing this. Citrus, dairy and wheat seem to be the biggest triggers
2)Chinese Medicine - I am an acpuncturist and have given her some herbs. When a child has red rashes at such an early stage, it is said they have fetal toxins which are passed on from the mother. It can be from diet, emotions, digestion from the mama. There are some great herbs for eliminating these toxins and for helping to nourish the skin. They are what mainly helped my daughter.
3)Daily baths - as many as you want during the day. The dermatologist recommended this and it really helps! 10 - 15 minutes, not too hot and use a really good moisturizer. (We use California Baby Moisturizing Cream or Shea Butter) He said two a day is best but my daughter isn't big on baths.