I noticed in your other post (which has been deleted since it was a duplicate) that you were concerned about infecting another partner you had last night.
First, you really need to start using condoms. Any of these partners could have something you could be infected with. Assume everyone is infected until you get proof otherwise.
As I said, the chances of you being infected by oral sex are low. If you're concerned, then test.
You can test for gonorrhea and NGU now (these are the most likely things you'd get, syphilis at 6 weeks (you wouldn't be infectious with this if you didn't have a sore), and hsv1 at 4 months (most people will test positive by 6 weeks.
Chlamydia isn't transmitted via oral sex. Gonorrhea can be, though.
Chances are really good that your partner didn't have it. Gonorrhea is fairly uncommon (especially when compared to chlamydia) and it's even more uncommon to find it in the throat. She's only had 3 partners, which makes her risk pretty low.
You could get NGU from oral sex. NGU is any infection in the urethra that isn't gonorrhea, and can be caused by normal mouth bacteria, things like strep or adenovirus (causes bronchitis and upper respiratory infections) getting into the urethra.
You could also be at risk for syphilis if your partner had any syphilis sores in her mouth. Syphilis is even more uncommon than gonorrhea, so I wouldn't worry too much about that.
You could also be at risk for genital hsv1 if you don't have it already. Keep in mind that 90% of those who have hsv1 never get symptoms, so unless you've tested for it, you could have it and not know it.
If you don't have symptoms, I wouldn't worry much or run out and test. If you've been sexually active, you should be testing regularly.