You see, when a doctor sees a patient presenting with a sore throat, oral gonorrhea is never thr first thing that comes to mind. Sore throat is very common, throat gonorrhea is uncommon. Doctors are trained to think about most possible causes first (when you hear hoofs, think horse, not zebra).
But a patient who is worried about STIs always exaggerates his or her risks. Throat gonorrhea or chlamydia normally is a low risk for those who give oral sex to a penis; your risk is even lower, a single exposure makes it even lower and very late onset of symptoms suggests your sore throat has nothing to do with STI.
I would only worry if your partner tests positive for gonorrhea or chlamydia. Otherwise, no need for any next move.
If you are super worried, you may ask for a specific throat swab for gonorrhea. There are two variants to process this test, growing cultures is more accurate, but it takes a week or longer.
Gonococci these days are usually not sensitive to penicillins, so your treatment probably won't interfere with test results.
Totally agree with this, and just to add, performing oral on someone with a vagina makes it even lower risk because nothing is physically in your throat like performing oral on a penis.
We can't tell you what is causing your throat symptoms, but an oral STD would be pretty far down the list of suspicions.