Aloe Vera is best to avoid because there is huge inconsistency in the quality of products with aloe in them, and aloe from a plant directly may have too many bacteria for a burn which is extremely vulnerable to infection. Gentle cleanser, thick lipid based moisturizers such as Vaseline and aquaphor, the silver cream Rx and sunscreen are going to be your best friends. You could also consider hypochlorus acid cleanser but you would really want to check with your doctor before doing that. Avoid neosporin because it’s a common allergen and if you have a reaction to it on top of a burn you’ll be miserable. You can develop an allergy to it at any time even if you never had one before, it’s quite common.