Sorry to say it but that is exactly what you have. That burning sensation and peeing multiple times, maybe even feeling like you still have to when your done?
It is actually not that common for men, most women will get one at least once though. It can result from dehydration. Drinking that soda made the problem worse.
Never fear though you can home remedy this and get rid of the pain within the next hour to three hours. Start drinking as much water as you can, but more importantly chug and I mean chug cranberry juice. Buy juice that has 27% cranberry juice in it and drink as much as you can over then next few hours. Keep doing this for the next few days and eating some aspargus will help rid you of the problem as well.
To help prevent the problem in the future you can buy cranberry extract pills from you local health food store.
I've had the pain your in and it sucks ass!
Good Luck!