In general, STD risks are low from oral sex--which is much safer than vaginal or anal intercourse.
Your symptoms are classical for a garden-variety upper respiratory infection, not an STD. For your specific questions: You are wrong about symptoms; most STDs of the throat cause no sore throat or any other symptom. When symptoms rarely occur, they generally are mild. Chlamydia almost never infects the throat; when gonorrhea is there, it clears up on its own in a few weeks--but of course antibiotics make it go away faster. Transmission of oral gonorrhea to a partner's genitals can occur, but is rare.
If you want to be 100% certain about all this, go to your local health department's STD clinic and have a throat culture for gonorrhea.
Good luck-- HHH, MD