Hello and hope you are doing well.
To begin wit keep a diary and make a note of his symptoms, this will help to track the allergen and avoid the same. For the psoriasis, apply constantly plenty of good moisturizing creams and alternate with steroid creams. Use a humidifier in the rooms to avoid dryness. Phototherapy for psoriasis is advocated for lesions not responding to topical ointments.
Hope this helped and do keep us posted.
Alternative medicine MD's are very good at diagnosing chronic ailments. I would go that route. As far as food allergies are concerned, kinesiology gets rid of them in jig time. I know because that was my personal experience. Old-fashioned allergists are not very successful, cost a bomb, and take forever.