Well, since you started taking the doxy, it's going to delay your testing times by a few weeks, since that could give you false negatives.
It would be very unlikely to get oral chlamydia from giving oral to a vagina, especially for 10 seconds, and if you've only taken one dose, I'd tell you to stop taking that unless your doctor told you to take it.
If you took one dose, it won't affect testing.
At about 5 days, you can get oral swabs for chlamydia and gonorrhea, but depending on how much doxy you took, maybe add a few days to that.
You can take a syphilis test at 6 weeks. The chances you got syphilis are less than chlamydia, probably, as it's uncommon in most developed countries.
I wouldn't recommend taking antibiotics you don't need. That's how resistance happens. Then when you actually need the meds, they might not work.