I don't think you were worried that your cough and sore throat were due to syphilis or any STI; if so, you were right-- no worries there. I agree with your doctor that you almost certainly had a viral upper respiratory infection -- and although I can't completely disagree with his reasoning about prescribing amoxicillin/clavulanate (Augmentin), I would not have done it, traveling or not. However, it did reduce whatever small STI risk you had from the event 10 days earlier. It definitely would have aborted incubating syphilis if you had been exposed; and prevent or cure most gonorrhea (although absence of urethral discharge and painful urination within 10 days is by itself nearly 100% proof you didn't acquire gonorrhea).

The 6 week interval for syphilis testing doesn't apply when there is no chance of infection. Antibiotics active agains syphilis do not convert positive tests to false negative results. They prevent positive test results by preventing or curing infection in the first place.

Those comments pretty well cover your two questions, but to be explicit:  1) There is no need to retest for syphilis. 2) Yes the treatment would have aborted syphilis, or cure it if it already had taken hold.

I hope these comments are helpful. Let me know if anything isn't clear.

HHH, MD