Hello, this is Dr. E. Greetings from New York! I'm so glad you posted your question for me to answer, and I aim to provide you with accurate info.
General good nutrition is key to any state of health - plenty of fiber, fruits and vegetables to ensure proper vitamins (no need for supplements). Psoriasis is auto-immune mediated, so avoidance of stress is key, along with good nutrition. I would avoid supplements as they can have untoward side effects and are not well controlled for quality. It is very common that the nails are affected by psoriasis.
I do wish your son well in his transition, Kathleen.