Your symptoms are vague, which I'm sure you know, and it's cold/flu/covid season, which can account for a lot, as can stress.
You could have gonorrhea or chlamydia, and you're right that oral chlamydia isn't nearly as common as oral gonorrhea, though the gender of your partner doesn't matter so much - chlamydia just isn't transmitted orally as often.
Syphilis sores appear at 3 weeks, on average, but can appear anywhere from 10-90 days. Most people will test positive on a blood test by 6 weeks, though it can take up to 90 days.
You definitely should test. You can get an oral swab for gonorrhea and chlamydia now, and get a test for syphilis at 6 weeks. Syphilis isn't all that common, generally speaking, in developed countries, though it is more common in MSM than other populations.
Let us know what the doc says.