First, I'll point out that oral gonorrhea rarely causes symptoms; probably no more than 1-5% get sore throat. Therefore, even in someone likely exposed orally, sore throat is evidence of a cause other than gonorrhea. Equally important, gonorrhea doesn't cause nasal congestion, drainage, or cough -- but of course garden variety upper respiratory viral infections regularly cause all these plus sore throat. So while I would recommend that all patients seeing their doctors be entirely open about possible exposures that concern them, and hence you should have mentioned your sexual exposure, it probably makes no difference in this case. I would also add, as you apparently know, that when persons at risk believe they are free of STDs, usually they are right -- reducing the chance your partner had gonorrhea.

There are no good scientific studies on gonorrhea transmission by cunnilingus. Transmission by fellatio clearly occurs; indeed probably 20-30% of urethral gonorrhea in men having sex with men is acquired from oral sex. However, you will appreciate the anatomic differences:  a meatus (urethral opening) contacting the throat of an infected partner is a very different exposure than the essentially external contact of the oral cavity by performing cunnilingus. The clinical experience in STD clinics is that pharyngeal (oral) gonorrhea is almost never found in men whose only exposure was by cunnilingus. (Indeed, for this reason pharyngeal gonorrhea is quite rare in men who only have sex with women.) Finally, for the same anatomic reasons, oral gonorrhea is not known to be transmitted to the female genital tract or by kissing.* So if you had it, there was little if any risk to your wife.

To your specific questions:

1) See above:  it is exceedingly unlikely have oral gonorrhea from the exposure described. 

2) Augmentin has not been carefully studied for gonorrhea, but usually would be effecitve. So if despite all that you indeed had pharyngeal gonorrhea, I estimate that treatment would cure 90-95% of infections.

3) Little if any risk to your wife; see above.

4) I do not recommend you be tested for pharyngeal gonorrhea.

I hope this information is helpful. Let me know if anything isn't clear.

HHH, MD

* The long term consensus among STD experts is that oral to oral gonorrhea transmission by kissing doesn't happen, or so rarely it can be ignored. However, one group of highly respected investigators recently have proposed that gonorrhea may be so transmitted more frequently than previously believed, especially among men having sex with men. The work is controversial and most experts remain skeptical, but we await further research on the topic.