Yes, it could be an STI. It might also be a urinary tract infection (unlikely with the UTI test), a prostate infection, dehydration, or a host of other things.
Receiving oral sex puts you at risk for gonorrhea, chlamydia, NGU, syphilis and genital herpes type 1.
The meds she gave you will cure gonorrhea, chlamydia and NGU, assuming you got doxy or azithromycin.
This isn't how syphilis presents, so I'd doubt it's that. You'd just get a round, open, painless sore.
Genital herpes type 1 happens when someone has oral hsv1 and gives oral sex. If you already have oral hsv1 (think cold sores, though most people with it never get symptoms), the chances of you getting that genitally are very low. You can still get herpes type 2, though that is rare from oral sex.
Relying on anyone that you don't know well - and sometimes that you do - to just say they are infection free is risky. Most oral STIs give no symptoms, so they might be infected without knowing it.
The urgent care doc did STI testing? Unfortunately, you'll have to wait for those results to see if you have anything.