Gonorrhea and syphilis can both spread through oral sex, but the risk is low compared to penetrative sex.
A test for gonorrhea will be accurate 3 weeks after the encounter, and urine needs to be hold in the body at least for a few hours in order to get an accurate result.
A test for syphilis is most of the times accurate 6 weeks after the encounter, but there are people that take longer to show a positive result, so in case of getting a negative one at 6 weeks, it would be interesting to repeat the test 3 months after the exposure.
Regarding the symptoms, I will tell you that sometimes, stds don't show any symptoms at all, and that's the reason why is good to test if we have encounters with people we don't know.