There is a chance for hsv2 and syphilis here, but not a huge chance if the frottage was just light touching.
It usually takes heavy rubbing or grinding, usually the kind associated with intercourse, to transmit hsv2, and syphilis needs a sore to be present to transmit.
Also, with both, you wouldn't have symptoms the next day. Tingling is most often associated with anxiety, and not an STI.
Since you forget about it when you're distracted, that lends itself to anxiety.
Herpes testing is loaded with false positives on the hsv2 IgG, so unless you see any actual sores, I wouldn't test for it. You can test for syphilis at 6 weeks, but if your partner didn't have sores, I wouldn't bother with that, either.
Good for you for getting the HPV vaccine. :)