What could cause stomach and chest pain then difficulty breathing followed by vomiting?

You need to go to the ER as soon as possible to be sure you are not having a stroke or heart attack. I am not trying to frighten you and it could well be an anxiety attack (they can sure feel like a heart attack.) There could be other reasons for this such as an irritated colon, twisted bowel, etc. Let the specialists in the hospital do their thing.