They probably come from the same root word. I've now read something about it (in Hebrew, alas!). They say that the word חמץ (the food you get rid of before Passover) may be related to the word מחמצת (the word for sourdough). Both of the words, חמץ and מחמצת, appear in Exodus in the context of prohibition. And sourdough, as well as מחמצת which is related to חמץ, is called sourdough by its taste. So yes, חמוץ and חמץ seem to be related. (:
Looking at the eight meanings of "sour" listed in https://en.wiktionary.org/wiki/sour. I guess when you say "literal" you mean meanings 1 to 3. Yes, these are חמוץ. By non-literal you probably mean meaning 4. You /could/ say חמוץ in this sense, it's sometimes used and it will surely be understood; but I think it's used less than in English. Note though that the idiom "sour face" was borrowed literally into Hebrew, פרצוף חמוץ, and is used often.