Lauren, I have been having this problem for over 10 years. It's extremely painful and also occurs right into about 10 minutes of running or so (usually a little past a mile for me). Sometimes I do end up having diarrhea, and but more often than not I don't. I don't think bowel movements are linked to the pain. It always occurs a couple of days to a week before my menstrual cycle, so I feel like that is a more likely link. Interestingly enough, I don't have them during my period. Often the pain does not stop until I am completely resting or sedentary. Does all of this sound familiar? I have no idea what it is either. I would really like to know. I meant to take Advil/ibuprofen about an hour before my intended workout. Maybe try that next time, if you find out what it is, please reply.
Also to other responders, it isn't diet, water or sodium intake. Like I said I've been experiencing this for a while and it happens no matter what.