Medical term for "holding urine for a long time"
A swollen organ may be described as distended if the swelling is symptomatic of a medical disfunction.
The purpose of most bladders is to collect and retain a fluid; if that fluid needs to be discharged periodically, and is not able to do so, then there is usually pain as a result of the distension.

Inability to urinate is known as ischuria or urinary retention, and could be the result of obstruction to the urethra, could be a failure of the bladder to fully contract during urination, or could many other possible causes.