I have a feeling that your gut have been seriously damaged by some Antibiotics you may have taken more than once in your life ... and that means it is going to take some time to fix it all...
One thing that may help is regular physical exercises, especially abdominal exercises, to strengthen your abdomen, and to strengthen your core muscles ... as those muscles can influence digestion, and help you improve your digestion.
Regular physical exercises also helps reduce stress ... and stress is a huge factor in Psoriasis and digestive disorders ...
So, if you are not doing it already ... start exercising daily, at least one hour every day...
It is also possible that you are allergic to something you are not aware of, something you are exposed to daily, like toothpaste, cosmetics, nickel, flame retardants in your home, wall paints, furnitures, carpets, a cat or a dog dander, birds, water, pesticides used inside your home to kill roaches, ants or other bugs, pesticides use outside your home as weedkillers, cookware you are using (nickel, teflon, iron, copper etc), black mold inside your home , etc.
You already know a lot about your own diet and your own food tolerance.
It is possible you have serious problem tolerating chemicals in your environment ... and that intolerance may affect your digestion, and your food tolerance.
Some people are vegan by choice .. others because that is only way to be healthy.
Listen to your body when it is talking to you!
I was "almost vegan" for more than 10 years, as I was able to consume fish, but not meat, no eggs or milk.
After several years of Liver Flushing ... it all changed. Now I can eat anything, but I choose to consume home made food exclusively, and I choose quality over quantity!