There are three ways (outside of a medical setting) in which HIV is transmitted. The first way is...…... UNPROTECTED INSERTIVE VAGINAL/ANAL SEX WITH AN HIV+ PARTNER.
Back in August, you engaged in unprotected, insertive vaginal sex. I'm well aware of the statistic you mentioned regarding the risk of exposure from a single encounter being "tiny." Regardless of how you try to tweak those facts, the bottom line is you STILL had a risk. If you've had a risk, it goes without saying you should get tested. If this woman did not insist you use a condom, it's possible she didn't insist her previous partner(s) use one either. This tells me she doesn't care about her own health, let alone yours. As to her claim of "perfect health, including STD's," I would take with a heaping teaspoon of salt on my way to the clinic to be tested.
As for your recurring tonsillitis, sinus and throat infections......you have obviously seen a doctor since you were prescribed antibiotics. Since these kinds of infections are notoriously very stubborn to cure, as you are finding out, I would strongly suggest you see an otolaryngologist. (Often referred to as an ENT...ear, nose and throat specialist)
Your friend back in August, whose HIV status is unknown, may very well have been harboring the bacteria which is now causing these chronic infections in you. Kissing WILL transmit these types of bacteria.
You are dealing with upper respiratory infections which are seldom, if ever, related to HIV......unless the HIV is left untreated.
In my humble opinion, I suggest you test for HIV with a 4th or 5th generation DUO test which will be conclusive 28 days post your last UNPROTECTED exposure, which was in August. You have stated you've since had PROTECTED sex with another woman, and this woman developed a throat infection after being with you.
So...…...my advice is for you to test for HIV for complete peace of mind and to see a specialist to clear up, once and for all, the recurring URI's. If you do have sex with anyone else before you are given the green light that all systems are "go," please continue to ALWAYS use a condom and do your partner a favor by NOT kissing her and sharing your various ear, nose and throat infections with her. I'm sure she'd be appreciative.
I'm sure everything will turn out fine and hope you'll keep us posted.