My wife is having trouble swallowing food and had short breath?

Many possibilities. Difficulty swallowing can be due to many things including neurological conditions, gastroenterology conditions (including reflux) as well as anatomical swellings in the throat. The first thing that needs to be done is a careful history with far more information about what she can swallow and what she can't. I would strongly suggest seeing a doctor for a complete history and examination.
Two separate problem. Difficulty swallowing most commonly relates to esophageal problems, either upper or lower. Shortness of breath may be related to congestive heart failure, pulmonary disease, or anxiety. There is one remote possibility. A large hiatal hernia which could compromise cardiac (heart) contractions. Obviously a diagnosis by either a GI specialist or a cardiologist is appropriate.