The itchy sensation could be because of Chlamydia and the discharge probably because of Gonorrhea, but sometimes stds don't show any symptom at all.
It's good to test after an exposure:
-3 weeks after the exposure get tested for gonorrhea and chlamydia.
-6 weeks after the exposure get tested for syphilis. If you get it negative, would be interesting to test again after 3 months, as there are people that take longer to give a positive result.
-Regarding HIV, which is rarely spread through heterosexual relationships nowadays in developed countries you have two possibilities: 4th generation duo combo ag/ab tes after 28 days, or a 3rd generation antibody test after 90 days.
-Herpes, you can also test after 3 months.
Basically, after an exposure with someone you don';t know, or someone you have met a shor time before, it's always good to go for a full std test.
All the best.