Firstly oral STI are not all that common or at least not as common as the internet makes out.
They are also by in large they are asymptomatic and don’t cause illness of any kind.
You risk via giving oral sex Gonorrhoea, Rarely chlamydia, Herpes and syphilis.
In the absence of sores on your partners penis the risk for herpes and syphilis is so low that if I was you I wouldn’t worry.
Chlamydia is rare in the oral cavity and once present clears on its own over a few weeks not causing problems. Further depending on your dosage of tablets it could have cured you if infection was present. Again I would not worry about this.
Gonorrhoea is fairly common in the throat it seems fairly well adapted to living in the throat. 90% of infections are asymptomatic so just on balance of probabilities I doubt this is why you have a sore throat. Cipro and Z-pack are somewhat reliable against Gonorrhoea and again depending on the dosage may have cleared an infection if present. If not like chlamydia it’s short lasting and dosnt normally cause any long term problems. On the balance of probability that you partner had gonorrhoea (unlikely) you caught it (not every sexual interaction spreads STI every time if infected) not self cleared in a month and the antibiotics not worked I don’t see a realistic chance you have or even had gonorrhoea.
Unfortunately I can’t hand on heart say absolutely no risk, I just say the chances are minute 1 in several million. If that’s good enough for you then move on. If not testing is the only way forward a throat swab can be done now for accurate results.
Please feel free to follow up or perhaps give me more information on the dosage of meds used so I can perhaps help more.