You should get tested, discharge could be a symptom of a std, but it’s usually present with urination and discomfort. You had an exposure with someone your not sure of their std status.
NO STDs give symptoms in just one day. Some of them never give them at all. But you had unprotected sex so you should test as follows :
-3 weeks after the exposure, for chlamydia, gonorrhea.
-6 weeks after the exposure for syphilis.
-3 months after the exposure for herpes.
Regarding HIV, if you go for a duo/combo ag/ab test, it will be accurate 28 days after the exposure. If you go for a normal antibodies test, it will be accurate 3 months after the exposure.