Can having diarrhea automatically mean you are allergic to what you ate?

Not necessarily: Diarrhea can be a symptoms of a food allergy, but is frequently associated with itching, hives and even vomiting. There are many reasons for diarrhea after eating including: intolerance like lactose (milk) intolerance, food poisoning, irritable bowel disorder, other GI disorder such as crohns or ulcerative colitis. A GI doctor likely has a much longer list of causes.