What Causes Growing Red Rash On The Chin Despite Using Fucidin?

Hello- I have had a rash on the corner of my chin, slightly to the corner of the crease by my mouth since April. I have never had any other acne, or facial issues to speak of as an adult. I am 41 years old. This rash all started when I was swimming with my daughter at the pool. It is painful raised rash, and has tiny pus filled beads that seem to come and go, as well as dry patches. It is currently very red and inflammed. I have been putting hot compresses on it to help relieve some of the pain. I have seen 3 different doctors since April..the first prescribed me a corticosteroid cream, thinking it was eczema. This cream worked slightly but never cleared it up. I went back to the doctor and the second prescribed me a cream for rosacia...this cream burned terribly and made the rash worse. I may have had a reaction to it, I only used it for 2 days and could not stand the pain. I am now on holidays, and went to another doctor who has prescribed me Fucidin Cream, an antibiotic, thinking the rash may be of bacterial nature. I have been using this cream for 2 days now and have not seen or felt any improvement yet. The rash is as its worst now, and I am extremely frustrated. This last doctor told me to be persistent with the cream for at least 4 days, if no improvement to come back. He thinks it could also be herpes , which I think is ridiculous, since this has been ongoing for 5 months and I have never had any issues like this before. I cant wait for up a year to see a dermatologist. I am wondering what your opinion might be?