I didn't take the time to read through all the responses, so if I repeat anything, just ignore it. I have a similar problem. This is a bit embarrassing, but mine is with my vagina. I have systemic candida, parasites, etc. If I eat anything with Sugar or complex carbs, I get horrible odor in my vagina. I am very self conscious about it. Obviously this is not your situation, but it works in the same way.
My gut feeling, no put intended, is that you have some kind of fungal or bacterial issue in your gut, i.e. parasites, candida, mold, etc. I would find a really good Naturopath in your area and start treating for these things asap. Might I suggest finding a Brimhall practitioner? http://www.brimhallwellnesscenter.com/
If you email them, tell them where you live and tell them you are looking for a practitioner in your area. Dr. Brimhall is an expert on these things. I am treating with a Brimhall practitioner in So. Cal. that I love. My problem is pretty complex, and my Dr. (Seth Mittleman) is wonderful - so caring and knowledgable.
I would also suggest that you lay off all Sugar of any kind, including fruit, alcohol, carbs like bread, flour, potatoes, rice, etc. and increase water intake. I'm sure you ND will tell you all this, but if you wanted to start before getting into once, this would be a good start. Good luck to you. I feel your misery.