Is it possible to have localized psoriasis?

Yes. When localized, psoriasis typically involves the scalp, elbows, knees, hands, or feet. Other common sites for localized psoriasis also include the navel (umbilicus), gluteal cleft (skin fold between the upper buttocks, armpits (axillae), and groin folds. A solitary scaly red patch, however, can be other things including nummular eczema, ringworm (fungal infection), or even skin cancer.
Yes. Some people get psoriasis in one area for years. Unfortunately for most is is scattershot, or even worse.