No. Your symptoms are by no means unique to the ARS. EWH
Welcome to our Forum. I'll provide some comments. I think that your "hit by a stray bullet" analogy is far too high. Your risk of getting hit by a meteorite is higher than your risk of getting infected from use of a contaminate razor in the course of getting a haircut. HIV is not spread in this way.
Your symptoms have some of the characteristics of the ARS but they are also a great description of the sort of symptoms which accompany any number of far, far more common, non-STD, non-HIV viral infections that are so very common in the course of day-to-day life and which, if anything, are more common among travelers. Given your lack of risk, I would not worry that they are due to HIV and I see no reason for concern or testing.
If your symptoms had been due to HIV, a test taken a week after they started would be positive.
Following acquisition of HIV, over 95% of infections can be detected by standard blood tests at 6 weeks and at 8 weeks, virtually all are detectable. I would repeat however that, at least based on what you report above, you have no reason for testing, much less concern.
I hope my comments are helpful. EWH
Thank you, doctor. I'd never had a cold before that hadn't affected my nose and chest. So that isn't unique to ARS, then?