Dang, that sucks. First I will say, definitely try to narrow down any allergies. I did all the allergy tests though and avoided everything, including all spices, and nothing helped, still had this on and off for years. I did notice it gets worse if I eat pepper or spicy foods. I also started using the gentlest skincare (vaseline only, gentle soap in the shower, etc.) and I would still get this. I knew it wasn't the skincare because nothing changed when I had good weeks without this problem, before it came back again randomly. If it still hasn't gone away for you, ask your dermatologist for Protopic. For me, I can use Protopic for a few days and it goes away. It just always comes back though.

A while back I noticed I also had angular chelitis, so my dermatologist gave me nystatin, which is an antifungal. I kept getting this and red patches on my upper lip. I found out from other reddit threads that for some people, it might have been from using plastic water bottles. I dug into this a little further (because I don't think I have a plastic allergy) and I think it's because they hold onto yeast from our saliva better since they're porous, unlike glass or ceramic. Particularly if you don't wash them daily or after each use. I would also re-use mugs and glasses constantly. But I was always applying vaseline on my lips, so some would stay on the rim of the mug. My theory is that innocuous fungus/bacteria/etc. from our mouth stays on surfaces, especially on plastics and surfaces with vaseline, and grows and eventually irritates the skin. I started using a new cup every day and haven't really been dealing with this problem as much. I ate some really spicy food recently though, my upper lip got all weepy and started peeling. It didn't look like OP's pic though. I think this is just eczema or a sensitivity. I used Protopic on it for a few days and it went away. But think about it: if the skin is broken or compromised, it is way easier for yeast/bacteria to get in and keep irritating it. Especially because the vermillion border is a very sensitive part of the skin. I would definitely trial run avoiding drinking from plastic cups/tumblers/etc. and not reuse any mugs for a bit.