I have frequent bowel movements right after eating, often loose, is this normal?

Frequent BMs After E. You may be describing gastro-colic reflex where the intake of food stimulates a bm. It may be triggered by a large meal and/or a fatty meal. Eating more often , smaller amounts with less fat content may help. See your doctor for full evaluation.
No. See your doctor for full history, exam, and possible tests. It may be easily avoidable with simple diet modifications.