I agree with Alicia. The times I have had this rash symptom with any of my three boys, it either cleared up with some attention to keeping the area dry or I had to get an anti-fungal from the doctor (since it is around the mouth, don't just apply any over-the-counter (otc) anti-fungal cream without advise from your pediatrician).
I can't say that what you are seeing is a fungal infection, but you sound like you are at the point of needing some doctor advise.
I have been able to call my child's pediatrician and talk to the doctor's nurse. Sometimes, the doctor wanted to see my child and sometimes he had general instructions on which anti-fungal (otc) I could try.
If you are breastfeeding, and you find that the rash is caused by a fungal infection, be wary that you might have the rash transferred to you. In my case, this just meant a little extra step to include putting the medication around the nipple area to 1) keep from getting the rash on me and 2) keep from re-infecting my child whether I showed a rash or not. Although, now that I think about it, my case was when my child had an infection in his mouth, as to what you seem to be describing, like a rash on his chin.
Anyway, good luck! You will get there!