Welcome to the STD forum. The chance you have gonorrhea or chlamydia from this event is zero for all practical purposes. Let's discuss each of these STDs individually.
Gonorrhea is a relatively uncommon STD in the US and is largely concentrated in especially high risk population groups Among most groups of sexually active women, well under 1% have gonorrhea. Of those who are infected, fewer than 10% have oral infection. So the odds your partner had gonorrhea that could have been transmitted by oral sex is under 1 chance in 1,000, probably far lower than that. And the chance of transmission, if she had it, probably is well under 10%. On top of that, 80+% of gonorrhea in the US is susceptible to ciprofloxacin, so your antibiotic therapy would have prevented most transmission risk. Finally, although asymptomatic gonorrhea occurs, it is the exception, occurring in under 5% of infected men. So absence of symptoms (urethral discharge, pain on urination) -- which would have started within 3-5 days of exposure -- is additional evidence you weren't infected.
Chlamydia is a virtual impossibility in this situation. You'll find lots of information on the web and elsewhere saying chlamydia is acquired by oral sex, but it's wrong -- even though such statements often come from apparently authoritative sources, such as public health departments. But the research is clear that chlamydia rarely infects the throat and, when it does, rarely is transmitted by oral sex (if ever). Why do so many information sources get it wrong? In my opinion, it is because there are many legitimate parallels between gonorrhea and chlamydia (symptoms, potential complications, etc), which leads people to assume that all aspects are similar. But they aren't. Finally, ciprofloxacin would have given you substantial protection. Cipro isn't a recommended chlamydia treatment, but it has substantial activity against chlamydia and probably would prevent an infection from taking hold.
I think that answers both your questions. In summary, you don't need testing and can be 100% confident you aren't infected with either of these STDs on account of the exposure described.
Regards-- HHH, MD
A related discussion, STD's from oral sex was started.