This symptoms sound quite severe and I suggest that you get in to see your primary care doctor
or your dermatologist
as soon as possible. You should not have to deal with these symptoms alone, especially if they are not improving.
Psoriasis as you know is a type of inflammatory skin condition that is an autoimmune disease, in which the body reacts to itself. The symptoms include red scaling plaques of inflammation on the skin, sometimes causing severe peeling of the hands or feet like you may be experiencing. Psoriasis can also cause a severe arthritis
and other medical problems.
There are many excellent treatment for psoriasis, which your dermatologist will be able to discuss with you at length after a thorough physical examination. The different types of treatment (steroid creams, oral immune suppressing medications, light therapy, etc) are all tailored to what type of psoriasis you have, how extensive the areas involved are, and what other symptoms (such as arthritis) you are experiencing.
Therefore, they first and most important step is for you to make that appointment! After confirming the diagnosis, and ruling out other conditions that could also cause peeling of the hands, your doctor will help you pick a treatment plan that works for you.