Unlike gonorrhea, chlamydia doesn't survive well in the throat and is rarely if ever transmitted by oral sex. CDC guidelines (which I helped write) state that there is no reason to test for it, and in fact there are no commercially available lab tests approved for the purpose. Anyway, if your throat were infected with chlamydia, the standard treatments would clear it up, presumably you already are being treated anyway. Bottom line: don't worry about it; just complete your treatment as prescribed.
Your question about rescreening is important. According to CDC guidelines, anybody with chlamydia should be retested, preferably at 3-4 months after treatment. Test-of-cure at 3-4 weeks is not recommended at all, except in special circumstances, e.g. in pregnant women or if atypical medications were used for treatment. But you are right in a sense: if test-of-cure is done, it should be no sooner than 3 weeks after completing treatment.
Good luck-- HHH, MD
Chlamydia of the throat is very rare b/c it's to hard to transmit via oral. That much I know. I doubt you were infected.
I completed treatment prior to the incident, just the 1g of azithromcyin. Should I ask the doctor for another dose just in case?
Azithromycin is very long acting and persists in the blood several days after single-dose treatment. If your reexposure occured within 4-5 days of treatment, there's no problem. If later than that, you should be re-treated.
Hate to split hairs, but the exposure was 6 days after the treatment. On the boarder, so should I just ask for another dose to be safe?
It's probably unnecessary, but that would be the safest approach.
A related discussion, Chlamydia of the throat
I wonder should I worry about getting treated again if I feel that the chlamydia isn't gone or is the medicine that good it just work on the first dose