Your lips are peeling because they are damaged and trying to scab over. The scab has to be left alone for as long as it takes. I've seen some bat shit crazy stuff on this forum recently and none of it is of any use. Fungal ? There is bacteria all over our bodies, in our mouths everywhere, it's not an enemy. We live in harmony with our environment, anti-fungals, ice, saliva,steroid creams, all they are doing is disturbing the wound and you start back at zero each time.