Can A UTI Be Sexually Transmitted?

Hi there, I m 19 years old and of good health. Around 3 days ago i had brief unprotected vaginal sex with someone who claims that they are not STI infected, and since this morning have noticed a rash on the gland area of the penis with blotchy red patches. I have had this in the past, even before i had first had sex, however, this time is accompanied by a sensitive and light pain when urinating. Also, my testicles feel sore and slightly sensitive. I didn t want to self-speculate but i considered that it might be balanitis or something a long those lines. Any ideas? (Also, the person has claimed they might have a Urinary Tract Infection so is there a possibility that i might just have an infection on my penis)