My son developed eczema when he was 1. I also breastfed and was very upset when I saw these patches develop on his shoulder, arm and leg.
I immediately threw out all chemical products in my household and purchased all natural laundry, dishwashing, bath soap, shampoo, cleaning products, etc. Within a week or so, his eczema started to disappear and has never come back (he is now 4).
It sounds like you have already done this and hopefully the eczema will clear up soon. For my son, his skin was reacting to the chemicals in the products I was using.
Your child is much younger and I hope you begin to experience similar success as he gets a bit older.