For me, my bad breath started in a very similar way. I would wake up with a strong acidic smell and in particular, a strong smell of orange peels or something like that -- it was very strange.
My smell is also like a really strong mothball, fecal-like or especially stinky shoes or socks smell.
I find though if I eat green grapes in particular it makes the odor worse or brings up a lot of acid so I just haven't eaten them or any fruit anymore for at least six months now. In fact I don't eat much at all - maybe a salad or a piece of chicken and that's it for the day. But still none of that has helped the bad breath at all.
My ENT told me once that acid reflux wouldn't produce bad breath for this long. This has been about 6-7 years I've been living with this hell.