Ugh! i know what that can be like. I had a recurring issue with my throat last year that didnt end up getting diagnosed, they said it could be strep, it could be mono, but none of the tests came up positive....so at least you know what you have! Two questions:
Does your doctor keep prescribing the same antibiotic? It could be that the bacteria in your body has become ''immune'' to it, and should try something else/a higher dosage.
Another thing to remember is to take the full prescription--say you have 10 pills to take, but your throat clears up after you've only taken 4 of them. It's important to take all 10, just to make sure that every little bit of the bacteria is killed.
I hope you all feel better soon!