Sore throat is a rare consequence of STD. Gonorrhea sometimes does it, but over 90% of cases are asymptomatic; and anyway, gonorrhea of the throat clears up on its own within 3 months. The first episode of oral herpes can cause severe sore throat for up to 3 weeks, no longer. Sore throat is common in primary HIV infection, but sore throat alone is never due to HIV. That's pretty much it for STDs and sore throat.
So the direct answers to your questions are: 1) No. 2) HIV causes sore throat for a few weeks at most; chronic sore throat isn't evidence of HIV. I don't know anything about chronic fatigue syndrome and sore throat. 3) I don't recall the last patient I might have had with this sort of complaint. Even if I remembered, I wouldn't say the cause here: whatever any particular patient had in the past is irrelevant to possible explanations in your case.
Bottom line: Clearly this isn't related in any way to STD or your escort exposure, unless due to anxiety over that event. Your personal provider is the best source for continued evaluation if your symptoms continue.
Good luck-- HHH, MD