I know you're vegan and stuff (I used to be until I got sick with candida and had to become a sellout lol) but the reason I mention it, is because high zinc intake usually helps with candida, you need a lot of zinc to help with fighting the infection particularly if you undermethylate (google pyroles disorder). As I mentioned earlier, gut dysbiosis is the reason for all auto immune and skin conditions (all disease starts in the gut, I know this for a fact). Allergies, asthma, all of that stems from having a permeable intestinal lining (leaky gut), so if this is an auto immune condition, healing the gut would be essential as well as cleansing the liver because the liver dumps heaps of toxins in to the intestines and if your intestines are permeable, the toxins get in to your blood stream and come out where ever they like.
Also, the lips are known to be the mirror for the intestines. Bottom lip is large intestine and top lip is stomach I think?
Maybe I'm totally off and it's all totally trauma related. But I think the way to go about this is doing the 'leave it alone' method, I use coconut oil and an antifungal HC cream with an Antibiotic cream and have just started a week's worth of Antibiotics on top of my antifungals because if there is a staph infection (I think there actually might me, when I first got EC is was just really bad chapped lips and I was stupid enough to touch it with my hands/fingers etc etc not even thinking about it being an open wound), so I'm covering the secondary infection route, that definitely would have made mine a lot worse, but I know deep down the primary 'infection' or issue at hand is candida in the gut.
(I get reactions to food all the time, I sneeze like absolute crazy when I used to eat any kind of fruit, starch, mushroom, fermented foods, nightshades etc) I'm doing an elimination, my safe foods are chicken, fish, green vegetables, saurkraut, suuuuper plain stuff. It might be helpful if you looked in to cutting your fruits down and maybe eating more greens and fats? It's hard to battle candida being vegan, but maybe it's worth a shot? Maybe that's not the root of your issue, who knows, I'm just sharing my experiences, our reactions seem super similar.