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 salty taste in your mouth probably is not a related symptom of the UTI/bladder infection (if that's what it truly is). Dehydration, infected salivary glands and various medications can cause you to have a salty taste in your mouth, but you really should go see a doctor about this.
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, and your doctor will also be able to diagnose your salty mouth.
Good luck.
LMNO