29y/o male with CONSTANT severe urine urgency that is not relieved by voiding. Nocturia. UTI negative. Antibiotics have not helped. What could this be?

Multiple issues: You must see a urologist and will probably need cystoscopy if that severe. Problems may ranges from irritable bladder syndrome, acute/chronic urethritis. a urethral stricture, diabetes insipidus ( not related to sugar) inflammation of the bladder neck, lining of the bladder and so it goes. Make an appointment today.
Urine urgency. Please as your doc for a referral to a urologist. You are young for this but it MAY be related to enlarged prostate. The urologist can arrange for a test to see how much you empty your bladder each time you urinate and check for constrictions. Peace and good health.