How long does it take to see skin improvement (in nursing infants) after cutting peanuts from diet??

I posted this response on your "new to all this..." by accident (I intended it to be on this post) I'm sorry that I don't have a certain answer for you, but I felt compelled to reach out to you anyway. I would think that within the next couple of weeks you would see some improvement. I had to maintain a dairy-free diet when I was nursing and when I would make a mistake, the resulting discomfort (crying nearly all the time) would last nearly a week in my daughter...I was told by a dietician that the milk protein would stay in my body for perhaps as much as a week, so there would still be some of it in the milk I was producing. Perhaps you are dealing with a similar situation?
My son is Peanut and tree-nut allergic. He outgrew an egg allergy. We found out that he was allergic by way of an anaphylactic reaction. Since he was 13 months old, we have maintained a house that is contains nothing but food that he can consume. It was a difficult transition, but once we got the hange of it, it is very livable. I trust that you will find solutions that you can live with as well...have faith that it will improve over time, and that you will get through this, even if he doesn't outgrown his allergies.