If your oral intercourse was protected, you couldn't have caught gonorrhea (in case is gonorrhea what is causing that) that way. But just to try to get more information, did you masturbate each other ? Because, if you did it and you got her vaginal fluid in your fingers and then touched your urethra, those fluids could have got into your urethra and cause the infection.
It's true that gonorrhea can cause a burning sensation, but without the withe discharge everything sounds extremely rare. But sometimes, stds don't show any symptom at all. It could also be caused by the physical action of performing oral sex on you, because of the friction between the condom and your skin.
As your intercourse was protected, there is no need of any test, unless your skin got in touch with lesions in that lady's lips (that could be caused by syphilis and/or herpes).
In case you still want to test, you can do it for herpes 3 months after the encounter, and for syphilis 6 weeks after the exposure. If you get a negative result for syphilis, it would be interesting to repeat it 3 months after the exposure, as there are people that take longer to show a positive result.