Have you considered calling the doctor (who wrote you the first prescription) and asking if he can just write you another prescription for a different drug, without a visit? If he’s already seen you, you took the medication exactly as directed, and are still having the same symptoms – he might just write you another script without a costly visit.
Might be worth a try.
Also, if you are a student (Just a thought due to the age) most schools have cheap, if not free health centers where they prescribe this stuff all the time. Or maybe look for a free health clinic. Most cities/counties have these services if you do not have insurance.
A lot of people swear by cranberries and other dietary changes… but their efficacy is debatable. If it is an infection that resisted a course of antibiotics, it can be pretty dangerous. As others have said, you don’t want it to travel to other parts of your body, or into your blood stream.
Bactrim is sulfa – so you’re right to stay away from it! Pharm student here – wondering what they prescribed you the first time, if you don’t mind sharing? It’s scary how many doctors prescribe drugs that are inappropriate choices for a given condition.