Why would it be that my sunburn is turning black and blue?

SImple basic care. Sunburn is response of the tissues to injury from solar radiation. It is simply inflammation which means increase blood flow to the area which has coloration. Do not use ice as this can injure already injured skin. Cool water soaks can help as can taking anti-inflammation medicines like Motrin or advil (ibuprofen). Avoid any further damage as this can cause scarring . Good skin cream applied daily/gently help.