Taking antibiotics is useful to keep bacteria away, as your body conditions would become to hostile for them. But taking antibiotics as a prevention can make them loose effectiveness as a long term effect.
My advice is to focus more on prevention. You can use a special kind of flavored condoms for oral sex, available in so many shops. They could protect you from gonorrhea (as chlamydia is not known to be transmitted through oral sex). Regarding syphilis, the protection wouldn't be at 100%, as if the other person had a chancre in her mouth, and that lesion touched your bare skin you would be at risk of getting infected.
All the best.
1000 mg of azithromycin would prevent chlamydia, if you were at risk for that, but probably not gonorrhea and syphilis, which you are at risk for.
Unfortunately, since you've taken the antibiotic, you'll have to wait to test for gonorrhea since the antibiotic can cause you to have false negative results. You should wait at least 3 weeks from the day you took the antibiotic. If you get symptoms - a discharge, pain with urination - see your doctor. They can test the discharge.
You can test for syphilis at 6 weeks. Some take longer to develop antibodies, but most will by 6 weeks, and if you haven't had any other symptoms, 6 weeks should suffice.