My DD broke out with an all over body rash at 12 weeks that sounds exactly like yours. We initially thought it was a berry allergy (through my BM), but elimination did not make it get better. After a month, it got slightly better, but never went away (and sometimes got worse), a different ped in my dr's office gave us a solution called Grier's Goo. I have no idea what is in it, and I can't find it online, but it works like a champ.
He basically said she has an allergy that is giving her eczema. The Goo helps get rid of it, but we are still working on finding the culprit - right now we are thinking milk and soy, but it's so hard to determine based on bm. Since it doesn't bother her too much, we are not too worried about it, but plan to be extra vigilant when we start solids.