What causes cramping & an urgency to have a bowel movement immediately after eating?

Irritable bowel: Sounds like irritable bowel or spastic colon. Your doctor can prescribe medication for that like Bentyl (dicyclomine) to be taken before meals and at bedtime.

Likely functional: Most times these symptoms represent a functional disorder such as ibs. However other etiologies such as ibd, small intestine bacterial overgrowth, bile salt induced diarrhea (to name a few) can result in similar symptoms and in the right scenario should be further evaluated. So see your doctor.