Welcome to HCM.Genital psoriasis
may be an isolated patch or multiple in number. Well circumscribed and localized and not diffuse. It is not difficult to cure and not very harmful. Usually not painful.
Anyhow a blood work up to rule out other STD/ HIV
is recommended. As you had only protected exposures the possibility of STD is rare.
Consult your Dermatologist
and follow his guidelines.