Firstly, I am very sorry you have this problem. I have widespread psoriasis but after 25 years am now having UVL therapy which is actually working. I am sure you know that prednisolone is a steroid (basically) and is prescribed for things like adrenal gland problems, Crohn’s disease, polymyositis, ulcerative colitis, etc. However, corticosteroids are occasionally prescribed for psoriatic arthritis. Prednisolone is also prescribed for problems like bullous periphigoid, which is basically severe blistering of the skin surface. The condition usually clears up after 4 or 5 months. So the steroid is used fairly widely, not just for psoriasis, and you should not be on it for a long time.
Will write again when I have more useful information.