I got the same problem. I started having this problem when I was in university.
Over the span of about 4 years, I saw about 4 different doctors and 2 dermatologists.
Short to say, the condition is called angular cheilitis.
Like you, things like tomatoes will trigger this problem for me.
There seems to be a lot of things out there that trigger this problem for me.
ie - soy sauce, tomatoes, salad dressings (caeser, italian) or any other foods which are high in acid.
I normally experience this problem in minor outbreaks, but like you, they normally heal up in 4 days - although there is a bit of discoloration left where the crack was.
What really fixes it for me is this.
I typically use a strong soap (ie dish detergent) and wash the sore out. Afterwards, I will apply a generous amount of petrolatum/petroleum jelly.
I will also supplement my diet with a good amount of vitamin b2 (riboflavin). You wont be able to find this as a standalone pill, but you will find it in vitamin b complex vitamins. A small amount will be sufficient. Eggs are also a good source.
After this, I will be healed up in 2 days....although the discoloration has never gone away