I had eczema on my lip and it left a red spot and white mark on my lip after the scab fell off?

A "red spot and white mark" are entirly normal after any sore or lesion that involved a break in the skin. It says nothing about the cause. If you're sure it was eczema, there is no reason for concern. If not certain, and if this was a single sore without other active eczema in the same area, it might be something else, like cold sore (oral herpes). But not because of the mark or spot left behind.