The risk of STDs from oral sex is low in general. There is some small risk from the exposure you describe, but there are no data to provide any sort of numerical estimate. Sore throat is not a common STD symptom. Statistically, the greatest risk probably is for gonorrhea, which can sometimes cause symptoms as early as 48 hours after infection. But oral/throat gonorrhea is usually asymptomatic. And no, oral STDs cannot travel through the body and then be transmitted through the penis.
If you remain concerned, visit your local health department STD clinic. You can do it at any time; gonorrhea testing is accurate within a couple days. Other STDs aren't common enough to worry about testing.
Good luck-- HHH, MD