Is it permissible to apply aloe vero on a burn on Shabbos?
The halacha is that a person that has a minor ailment may not put medication on it. The reason is because he may come to chop up other herbs etc., which is meleches tochain. I am assuming that the burn is not so bad that the person is bedridden as a result. If he would be bedridden as a result, then he would be considered a choleh kol gufo, and he would be allowed to apply the aloe vera gel in a permitted way, but this doesn’t seem applicable to your case.
Rashi Shabbos 53b D:H Meshum, O:CH 328-1, 20.