What does chest pain from swallowing and eating mean?

Esophagus. Esophageal spasm, inflammation (esophagitis), ulcers or stricture (scarring forming a narrowing) can all cause chest pain from swallowing. Pain with swallowing or difficulty swallowing are considered "alarm symptoms" and warrant an evaluation and treatment. Sufficient damage over a period of time increases risk for barrett's esophagus, considered to be a pre-cancerous condition.
Esophagitis, ulcer. A proper diagnosis requires an endoscopy, a visual examination with a gastroscope. These symptoms can be signs of stomach ulcers, and the severity of the problem can only be evaluated by a gastroenterologist. Diet may help, but the proper medications are necessary to prevent progression.
Likely fm esophagus. Pain localized near the area beneath the breast bone generally reflects irritation to the esophagus (swallowing tube) as it enters the stomach. Stomach acid can push up the esophagus & leave behind a sunburn like change to the tissue & cause pain with feeding. Cafeine, sodas, chocolote, acidic foods&eating close to bedtime all can aggrivate the process. Disc with your dr as diet chg or meds can help.