It’s called angular chilitis and you have got it real bad. Are you following the forums protocol with the strict diet? If you are not and are eating things like brown rice, corn, etc. this is likely the cause of your outbreak. Candida thrives on a poor diet and you need to change the environment of your body internally.
Additionally, are you taking anything to heal your liver? Mouth conditions are tied directly to the liver per my naturopath and if you are not supporting the liver or protecting it, then it is ailing right now.
I’d consider going in for acupuncture which will clear it up within a day or two. There are two points above the mouth next to the nose that will heal this easily from my experience.