Hey Michael. Did the antibiotics not have any effect? DD has eczema on her chest (and now the back of her neck in more recent times) that got a bit infected from all her scratching. She was put on antibiotics for a different reason, but they cleared up the infection and we used a prescription cream called Advantan and within a week it was really clear. After we stopped using it it has become dry again, but I'm not going to use that cream until it gets really bad as I've no idea what's in it!!!
You are doing the right thing by getting it checked out properly by a derm. Continual use of cortisone creams on thin skin is not good (can cause the skin to get thinner) so its good to try to find the cause rather than just lather that stuff on. But I wonder if your poor DD has a bit of a staff infection there if it is so full of pus and not getting better? Might be worth asking about some stronger antibiotics?
The only other thing I'll suggest here is that if your wife is going to do an elimination diet while bfing, please talk to a doctor or better still a nutritionist before excluding too much from the diet - it is best to have help with these things so that she doesn't become malnourished herself. It is so important that she looks after her body while bfeeding
Take care, and I'll keep an eye out here to see how you're doing. Let us know how the second opinion goes.