Is there a connection between a constant need to urinate and now having blood in urine?

Urinary tract infect: Yes. Some condition like bladder infection/ urinary tract infection can give you sense of urgency-, increase urinary frequency, burning sensation when urinating and can have blood in the urine. Other irritation on the urinary tract -like stone, bladder irritation-can do the same. Go to see your doctor now to get checked and treated. Antibiotic will be needed if you have bladdder infection.