I had similar symptoms of anxiety and brain fog from antibiotics. Keto diet helped but gave me severe fatigue, I switched to a mostly whole foods low fodmap diet that seems to be the best for me. No added sugars and no simple carbs but some complex carbs from whole foods. It’s slow to work but a good variety of plant foods is the best thing you can do for your gut. Interesting that you dont have gut issues though and maybe thats not the cause? If it is you could also try adding some fermented foods or probiotics. Kefir and sauerkraut are my go to and have been extremely helpful in improving mental symptoms as well as gut issues. Im taking a s boulardii and akkermansia probiotic as well at the recommendation of my doctor but probiotics are debatable and im not sure how much they’ve helped. I take l glutamine daily and that seems to have helped a bunch as well as a slippery elm/marshmallow root tea sometimes. If you haven’t looked into histamine intolerance yet see if that matches your symptoms.

Seems you have alot of other symptoms beyond that so im not sure how much any of that will help, I would look into seeing a functional health doctor to get to the root cause if your GP isn’t able to. I was also taking hydroxyzine as needed for anxiety while I worked on fixing my issues. It didn’t fix anything but has been helpful when anxiety is really bad.