Many therapists now believe that eczema and psoriasis (and many other immune system disorders) are caused by leaky gut syndrome. If you have any gut problems at all you should consider if they are related to issues with your skin.
The theory is that breaks in the delicate gut wall allow food particles and toxins into the blood stream. This is very plausible because the gut wall is vey thin and is surrounded by blood vessels that absorb nutrients from the food we eat. It is thought that simple problems like an overgrowth of yeast (eg. candida) in the gut, which anchors itself to the gut wall, can cause gaps to occur. Also an imbalance or lack of good bacteria, which lubricate the gut can cause inflammation, and consequent leaks, which could also allow foreign particles to get through. Clearly any IBS, Colitis, Crones or other inflammation can also lead to leaky gut.
Once the immune system detects these normally acceptable proteins which are now in the wrong place, it sees them as invaders and it makes antibodies to fight them. This can cause allergies to food that should be acceptable, or the body can confuse food proteins with proteins that are found in the body's own tissues, and so the body starts attacking itself. This is the definition of an auto-immune disease.
Because the blood that absorbs nutrients from the gut goes straight to the liver, if that blood contains excessive toxins and foreign particles the liver will become overworked and may start to fail. This in itself may be implicated in eczema and psoriasis.
Leaky gut can be improved by using certain amino acids, glutamate powder, slippery elm, gelatine, stock (or bone broth) probiotics and by eating a healthy diet high in fibre and low in gluten. Be aware that taking probiotics it's not always a simple process. The range of bacteria in the gut has to be in balance so you may take one type of probiotics and not see an improvement. There are many different strains of bacteria and they appear in different brands of probiotic powders and tablets, you may have to take different ones before you see a difference. A nutritional therapist can help you with this, don't give up if you take one brand and it doesn't help.
The liver can be healed by avoiding toxins and taking liver boosting supplements. Your doctor can test you for candida, but be aware there are other parasites and yeasts that cause the same symptoms that they will not test for, so if you suspect you have candida, don't take a negative test as the end of the story.
There is much information about symptoms and treatments of these issues available, so you can do your own research, but a qualified and reputable nutritional therapist will be able to diagnose and treat these sort of issues safely and effectively. The NHS do not treat leaky gut.