Have you ever had a problem with severe nausea? Is it possible that bacteria from your lower intestine has come in contact with your throat/mouth? If so, it could have colonized your tonsils or the soft palette on the roof of your mouth. Once there, it can be extremely difficult to get rid of.
If any of this sounds right, the bacteria could be producing hydrogen sulfide, the gas that gives poo its smell. Find a doctor who is willing to test you for the gas and prescribe the right antibiotic. If you can't find one, there are some steps you can take in your diet to slowly eliminate the colony over time and restore your digestive tract to normal.