If there were cracks or breaks in your lips, then that is how bacteria like staph and candida would enter. Staph and candida are very common in the environment and even healthy people can live with these bacteria on their skin - its only when the skin is broken that they have a chance to enter and cause damage.
As a result of the infection, your lips become inflamed. Inflammation is the body's natural response mechanism as it tries to fight the infection. The crusts on your lips are forming because due to the inflammatory response your skin cells in the lips are producing skin at an abnormal rate.
The problem with EC is that even if you get rid of the infection, the inflammation can continue because it has become chronic and the cells still 'think' they need to be producing skin at an abnormal rate.