Cough for two weeks. some sputum. occasional nausea. developed after having oral sex with someone who has had multiple sex partners. do i have an std?

Coincidence: It is likely a coincidence that you are having these symptoms after oral sex. Typically, stds transmitted during oral sex do not result in a productive cough. More commonly, the symptoms are open sores, symptoms in the mouth, or a sore throat. Your symptoms are likely viral. Treat the symptoms, drink fluids, and get some rest. See your doctor if it doesn't get better or new symptoms appear.