I am aware that the chumash was divided, some time ago, into chapters by the goyim, and for some reason (Political correctness, or to lessen confusion??) we use these chapter and verse designations today. My Question Is This : Is the same true for the rest of the tanach ? Are the chapter and verse designations from the goyim or not ?

True, the Jewish division of the Tanach are the "open" and "closed" parshiyot (paragraphs), not the known verse/chapter division. Since there is no Avoda Zara in the chapter division (Chochma Bagoyim Ta'amin) it is permissable to use it. Rabbi Ro'i Margalit.