A newlywed is a person who's recently gotten married. If you just got married this morning, you and your new spouse are newlyweds. Congrats!
Some people will consider you a newlywed for several years after the actual wedding. The word comes from a popular early twentieth century comic strip about characters named Mr. and Mrs Newlywed called "The Newlyweds and their Baby," which was published in a New York newspaper.