Chest pain that radiates to back especially after eating. Can feel every bite of food going down throat but so painful. I'm very hungry but can't eat.?

Esophagitis? Persons with hiatal hernia, esophageal disease or irritation can present as you relate. Dysphagia is very unpleasant . Record dates, times, foods, etc likely need agastroenterologist to help your pcp solve the issue.
Need evaluation. You symptoms suggest esophageal disease. Please see your doctor and seek a referral to a gastro-enterologist for an imaging study or endoscopy. See this site for more information. http://www.webmd.com/digestive-disorders/tc/difficulty-swallowing-dysphagia-overview.