It is impossible to tell if the Z-Pac will cover the bladder infection without a urine culture. Many bacteria are resistant to the newer drugs like azithromycin, and only an older drug like Bactrim-DS will cure them. I suggest you see your doctor for a culture to make sure your current drug is going to work.
Actually there isn't a sure-fire way. The doctor will need to do a urine test. If you are having symptoms of burning, urinary frequency, a feeling that you have to go but can't, it is probably a urinary tract infection. If you are having itching and burning in the vaginal area and perhaps a white discharge, this is more likely a yeast infection secondary to the antibiotics. You can try some over-the-counter yeast infection treatment such as Monistat or GyneLotrimin if you are having yeast infection symptoms. There is no antibiotic available over the counter for a bladder infection, and they generally just get worse with time, not better.