Can a person have a stomach or intestinal cancer that only causes pain during and after eating? if so, why?

Many possibilities: The type of pain during and after eating may help point to a cause, however cancer would be an unusual cause for this sort of pain. More likely causes include: gallstones, food allergies, esophageal spasm, vascular insufficiency, partial obstruction/blockage, pancreatitis, irritable bowel syndrome, etc. You should see a gastroenterologist for additional studies.