Is it possible it's coming from your stomach? Sounds like it if food stops the problem.
Seeing a gastroenterologist is advisable if you have already had a dental checkup and cleaning. If not, I would start there.
Best to you,
Bad breath can be caused by a number of reasons - one reason could be underlying dental problems such as decay or gum disease, another could be dry mouth due to medications or other lifestyle factors. A systematic disease,medical condition or tonsilitis could also cause bad breath.
I would first recommend a visit to the Dentist and if nothing is found then a trip to your GP.
Bad breath is very common.