Stomach or chest pain could happen if you eat too fast or have an occasional greasy meal. Generally though, eating shouldn't cause pain afterwards. Constant abdominal pains could be signs of food a intolerance or allergy -- or possible acid reflux. Visit your doctor right away to get a proper diagnosis and treatment, before symptoms become more serious.
Intolerance or Allergy
Belly cramping following the consumption of a particular type of food is likely a signal that your body doesn't tolerate it well. You could have an intolerance, such as gastrointestinal discomfort related to lactose intolerance after consuming milk. Or if your stomach pain is associated with a rash, swelling or itching, you might be allergic to the food. (ref 1/severe symptoms)
If your pain is higher up in your chest however, you may have acid reflux. This condition occurs when the sphincter at the base of your esophagus doesn't close properly. Stomach acid starts flowing upwards into your esophagus, causing severe chest pains. (ref 2/what causes GERD) Caffeinated drinks, greasy foods and spicy foods can be triggers of recurring acid reflux. (ref 2/avoiding foods...)