Constipation can be due to millions of different diseases. You had unprotected oral sex, which exposes you to gonorrhea, syphilis and herpes. The risk is really low and your constipation will probably be caused by other things, but it would be interesting to test for all those ones, as I show you:
-3 weeks after the encounter, for gonorrhea.
-6 weeks after the encounter, for syphilis.
-3 months after the encounter, for herpes.
If your test for syphilis comes back negative, it would be interesting to repeat it 3 months after the encounter, as there are people that take longer to show a positive result.