What can be done to heal a sunburn faster without aloe?

Cool compresses.: Try to nsaid's & acetominophen orally and cool compresses to the skin.

Simple Care: 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.