2. How worried should I be that she had oral gonorrhea and passed it along to me?

3. Would I have developed symptoms?

I then had oral sex with my wife around 3 weeks later. A few days after that she developed a sore throat, fatigue, and a minor cough. This lasted about 36 hours and symptoms were reduced with DayQuil? Do I need to worry I gave her something? 

This was a very safe sexual encounter. The amount of online discussion about STI risk from oral sex is way overdone. Reading sites like Reddit, one easily can come to believe that oral sex is high STI risk. It is not. In fact, it's low risk for all STIs and virtually zero risk for some. As it happens, gonorrhea is among the more common possibilities from oral sex, but even this is uncommon. I would say there is under one chance in millions you have gonorrhea; and just about as low for all others as well. First, even among the most sexually active partners, including female sex worker, at any point in time the large majority have no oral STI that can be transmitted. And when oral STIs are present, they are transmitted rarely. And escorts (expensive female sex workers by appointment) generally have low STI rates:  they are aware of the health risks, take steps to prevent them (like condoms and frequent testing) and they tend to have low risk partners (men like you!). All in all, your STI risk was higher from the condom-protected vaginal sex than it was from unprotected oral -- both risks being very low. To your specific questions:

1. As a rough overall estimate, maybe around one chance in 10,000 of any STI. The main risks are nongonococcal urethritis (NGU), often from harmless oral bacteria; herpes due to HSV1; and gonorrhea. Syphilis is theoretically possible, but extraordinarily rare in female escorts and not often transmitted orally. Finally, absence of symptoms a month later is strong evidence you acquired none of these.

2,3. Among all escorts, probably no more than 1% have gonorrhea at any point in time. About 5% of those with gonorrhea have it orally; this comes to ~1 chance in 2,000 she had it. When present, maybe 10% chance of transmission -- so now we're down to 1 chance in 20,000 you were infected. The vast majority of urethral gonorrhea causes obvious symptoms within 3-5 days. Absence of pus drip from your penis and painful urination are, all by themselves, nearly 100% proof you didn't acquire it. Considering all these predictors, there's no more than one chance in many million that you have it now.

Neither gonorrhea nor any other STI causes the symptoms your wife has had. Almost certainly she had a common cold, or maybe a minor case of covid. I see no need for either you or your wife to be tested for gonorrea or any other STI.

I hope these comments are helpful. Let me know if anything isn't clear.

HHH, MD