I took photographs of someone else’s artwork. Is it OK for me to use them any way I wish, since they’re my photos?

Maybe yes, maybe no — it depends on the age of the artwork. Works of art and architecture are copyright-protected if they were published in 1923 or later. In these cases you will likely need to get the artist’s permission. Architectural works produced in 1990 or later are also protected. Works that aren’t protected are art and architecture produced before these dates or that include subjects that fall outside of these categories.