You might have a nutritional deficiency (perhaps caused by a food intolerance that has caused damage to your stomach lining; maybe celiac disease) and/or a sensitivity to certain chemicals (such as sodium lauryl sulfate, and/or such as other chemicals that remove oil from skin).
I have a couple pitted nails, and I don't seem to have any psoriasis. When I stopped using SLS and started a gluten-free diet, my nails at least stopped getting worse. I don't know if they're getting better (but the one that had been developing gunk underneath stopped, and I think they look a little better than before). I thought it was nail fungus at first, but the doctor was skeptical. We'll see if this helps overall, though.
Do you have any other symptoms? Do you have gum recession? Sodium lauryl sulfate sensitivity could be at least partly responsible, if so.
Do you have known digestive issues (gas, bloating, distended belly, nausea, etc.) or problematic stools of any kind (i.e. oily, mucus-laden, overly smelly, extremely large, green, diarrhea, constipation)? If so, I would consider celiac disease even more.
Do you have skin problems that aren't psoriasis? e.g. acne, really dry skin, eczema, or such? What about growth issues?
Anyway, just some food for thought. I hope it helps.
Also, I might recommend researching minerals—you might be getting too much of one and inhibiting another.