I see nothing medically urgent about the need to evacuate the bowels when you feel the urge. Doctors tend to treat constipation (difficult or infrequent bowel movements ) and diarrhea ( loose, watery stools more than three times in one day) as medical problems. But it sounds like your bowels are fairly healthy.

Can you close or tighthen the sphincter in order to prevent an accident. Can you do this? To check the sphincter muscle of the rectum and to follow up on your other questions, you might want to see a GI specialist...but I really don't think that you've got too much to worry about.