I've some things that suggest that an intolerance can affect your mental health, however I would also reiterate the point that mental health affects your gut (and how well it tolerates stuff!) - big time.
I think most of the things on your list are foods described as high FODMAP (Fermentable Oligosaccharides, Disaccharides, Monosaccharides and Polyols). - These are basically food stuff containing certain types of sugars that are harder to digest than others. -
https://en.wikipedia.org/wiki/FODMAP - worth doing a bit of research.
A low-FODMAP diet is often recommended (by doctors) to deal with the symptoms of IBS and it helped me a lot. Once things have calmed down a bit for you, you may find that you are able to reintroduce some of those foods in small amounts without them affecting your anxiety so much. Worth keeping a food diary too, as it will help you keep track of what most affects you in the long term.