Welcome to the forum. Thanks for your question.
The important information here is your negative HIV test result. Depending on the exact test done, it is either 100% conclusive (if you had a duo test for both HIV antibody and p24 antigen) or very close to it (95%+ reliable if you had a stand-alone blood antibody test). The HIV blood tests are among the most accurate and reliable diagnostic tests ever developed, for any medical condition, and they are very robust -- i.e. almost no external conditions (medications, other illnesses, etc) have absolutely no effect on test reliability -- and for sure your azithromycin, tylenol, etc make no difference.
I could get into your exposure history and symptoms, but there's no need: because the lab tests are so good, the results always overrule symptoms and exposure. Even if you had had an especially high risk exposure (you didn't) or if your symptoms suggested HIV (they don't -- acute HIV doesn't cause cough), the test results rule and prove you aren't infected.
Below is a thread that discusses times required for definitive results with the standard HIV tests, and the reasons that official advice still suggests an antibody test at 3 months for definitive proof, even though earlier testing is reliable. Depending on the test you had, you may decide to have another 2-3 months after the sexual exposure. But in the meantime, you can be very confident you don't have HIV. All is well.
Here's that other thread:
http://www.medhelp.org/posts/show/1704700
I hope this has been helpful. Best wishes-- HHH, MD