Rash for months now 🤷‍♀️

I'm stumped ladies. My son has had what I thought was a drool rash for about 3 months now. The doctor agreed that it was a drool rash. She initially told us to try a diaper rash cream or Vaseline on it. We tried both for about 2 weeks each, and nothing. He has been to the pediatrician twice for it, and she finally gave us a prescription for a topical antibiotic and said if it doesn't go away then I need to go to a dermatologist 🤦‍♀️ any tips as to what it is and how to get rid of it? He doesn't seem bothered by it at all. He has had no diet changes and he honestly has been teething for about the entire 3 months.