My cat is balding

Her hair keeps getting off from certain areas of her body and due to which I have also developed some sort of skin diseases known as Psoriasis Rosea. I took her to the vet, he gave a shampoo and oral medicine for her. But my itch keeps getting worse. She stills has those spots but I see an improvement. Does anyone have any idea if sth like this happened to them?
She is my ESA and I cannot part from her.