Most of the time, men who have common sexually transmitted infections like gonorrhea or chlamydia will have abnormal findings on their urinary samples, such as positive white blood cells. Therefore the fact that you had a normal urine sample is reassuring, but I don't think it completely rules out the possibility of a sexually transmitted infection.
It is also true that some fungal infections will glow under a black light. However, the most common fungal species that would cause an infection at the tip of the penis are not among the species that would tend to glow. Additionally, fungal infections of the penis are relatively uncommon in otherwise healthy men, although they do occur in those with immune problems such as HIV or chronic medical conditions like diabetes.
Taken altogether, I think you intuition to want more definitive testing for a sexually transmitted infection is correct. There are simple tests for both gonorrhea or chlamydia that can be done from either a penile swab or a urine specimen. If you go to see your primary care doctor
, I am certain that they would be happy to run these tests for you, especially if your symptoms do not go away with the fluconazole.