How do I make the sunburn on my face not peel and heal faster?

Simple Treatment. 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.
Emollients.... ..Or Hydrocortisone cream may hasten its resolution, but mostly, you just have to ride it out and wait for it to resolve. Next time, apply a good sunscreen lotion and reapply it frequently.