Both gonorrhea and chlamydia are detected in a urine test. They draw blood for a syphilis test and here are the tests used to diagnose genital herpes https://www.webmd.com/genital-herpes/genital-herpes-diagnosis#1. No sores is a good sign that herpes is not a factor for you.
A normal urinalysis would show if you had signs of infection, but if they don't specifically look for gonorrhea or chlamydia, it might not be found. You should follow up with your doctor to make sure these specific tests were done. Ask for a copy of the results.
Chlamydia isn't a risk from oral sex, but gonorrhea could be. You could also get NGU, which is a bacterial infection in your urine. This would be found on a regular urine test, though.