Yes this happens to me occasionally. One dermatologist told me it's because my lips sort of press together at the corners so say I eat something salty, it can get kind of "trapped" there and irritate. Anyway the best solution I found was 1) don't touch your lips with your fingers unless you have just washed them, 2) wipe your mouth with a clean napkin very well after eating, 3) avoid really outwardly salty foods like tortilla chips, 4) Keep Aquaphor on them at all times (it's a clear lotion that looks like vasaline but it's more water-based...just use it like chapstick but the nice thing is if it gets on your skin it doesn't seem to cause breakouts like vasaline would), 5) Keep drying face products (like acne gel or toner) away from the edges of your mouth.
Also, just in case it's some kind of fungus or bacterial thing, I'd throw out all lip products you currently have and start fresh. Also, watch for skin sensitivities (and you can develop ones you did not have before). One of your lip products could be causing it.