Silver sulfadiazine good for sunburns?

Overkill. Silver sulfadiazine is used for significant second and third degree burns. It would be overkill for a sunburn unless is was an unusually severe burn.
Expensive overkill. Sunburn is response of the tissues to injury from solar radiation. It is simply inflammation which means increase blood flow to the area to promote healing. 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 helps.