Other than sores, my symptoms were identical to yours... itching, draining, pain.
It took two visits to my local VA clinic before they diagnosed it correctly as both an inner ear infection and irritation of the ear canal.
I had been swabbing my ear canal with an iodine solution. They advised against that since it causes drying of the skin.
They prescribed an antibiotic for the inner ear infection, and ear drops which contained an antibiotic.
I completed treatment a couple days ago, and everything's now back to normal. Hope it lasts!
I would advise seeing different physicians, get second, even third opinions.
Perhaps you're being given the wrong antibiotic?
My ears just started draining a clear liquid. Saw my primary care dr. She prescribed a steroid ear drop and 2.5% hydrocortisone cream for my ear lobes which had crusted up from the drainage. I originally thought it was coming from my lobes because I had worn pierced earrings I hadn't worn in a long time. But I also wear hearing aides so reading some of the previous posts was interesting regarding possible cause and effect. I hope what the doctor ordered works for me. Just concerned about the sudden drainage.