Probably not at 3 days, and at most, the trimethoprim would inhibit or slow the growth of gonorrhea or chlamydia, not kill it, so you would probably still show as positive.
I don't know what your risks were, or symptoms, or if they actually tested you for a UTI, but if that treatment doesn't work, you can test again after being off the antibiotics for a couple of weeks.
Trimethoprim should not make a difference