Actually, for what it is worth, although many different antibiotics are known to decrease the effectiveness of birth control
pills, Bactrim is not typically considered to be one of the antibiotics that has this side effect. In fact, this is part of the reason why Bactrim is so widely used in young women with urinary tract infections - the fact that it typically does not interfere with contraception.
Also, having a UTI in and of itself will not interfere with the effectiveness of your birth control pills. The urinary tract and the reproductive tracts are physically separate from each other. In particular, the ovaries, where the birth control pills primary work, are located inside the abdomen and should not be affected in any way by inflammation from an infection inside the bladder.
Therefore, I advise you to continue taking your birth control pills as prescribed and also to take the antibiotic as prescribed. You should also continue to follow up closely with your OB GYN doctor
or your primary care doctor
and let them know how you are feeling and if the infection is clearing up as it should within a couple of days.
I hope that you are feeling better soon!