There is some risk here.
Giving oral to someone with a vagina is very low risk, but there is a slight risk for oral gonorrhea, chlamydia and syphilis. The risk is low enough that I wouldn't worry about it.
Getting oral puts you at risk for gonorrhea, chlamydia, NGU, syphilis and genital herpes type 1, if you don't already have it orally.
The risk is low, but definitely it's still possible.
Burning with urination at 2 days, especially if it's not consistent, is probably something else - anxiety, mild dehydration, irritation from alcohol or caffeine. Try increasing your water and decreasing alcohol and caffeine and see if that helps.
You can test for gonorrhea, chlamydia and NGU at 5-7 days. You can test for syphilis, which is uncommon in most developed countries at 6 weeks. If you don't get any sores, I wouldn't bother testing for herpes. The tests are unreliable enough that it isn't worth it just for oral sex. It can also be positive for hsv1 if you have it orally, and it doesn't tell you where you have it, just that you do.