Except in a few geographic areas, syphilis is largely absent in heterosexuals in the United States--so the odds your were exposed to syphilis are low. Also, the advice you received about syphilis testing is accurate. Most people with syphilis do develop overt symptoms they would recognize.
So in summary: with very low riskyou were exposed, plus no symptoms, plus negative blood test at weeks, you can be 100% you didn't acquire syphilis during the encounter you describe. No, you do not need another syphilis blood test.
Best wishes-- HHH, MD