Three weeks treatment likely would cure you, but to be safe, I recommend you be retested a few weeks after you finish treatment
to be sure you were cured.
Perhaps your provider intended the treatment
to cover chlamydia plus certain other infections, in which case cipro might be OK. But to be safest, it would be best to also ask for a single 1 gram dose of azithromycin. Then you wouldn't need to worry about retesting.
Well, the last statements needs clarification.