Sounds like a urinary tract infection or a bladder infection. "Urgency" is a common side-effect of both of those. Urgency is when you feel like you REALLY have to urinate, but then either nothing comes out, or it comes out slowly with little force. The UTI/bladder thing you have going on (if that's what it is), should be pretty easy to clear up with a wide-spectrum antibiotic.
HOWEVER, it could be an STD, so if antibiotics don't work, you should get checked out for STD's. Actually, if you've had unprotected sex, you should be getting checked regularly anyway!
Get thee to a doctor!!!
Good luck.
LMNO