Relax--you will be fine. These color and texture changes are temporary. Some people feel that putting Vitamin E on speeds healing. I don't know for sure if this is true, but it's harmelss and may help.
Another statement you often hear is that sun, or tanning, delays healing. I'm not sure if that's true either, but sun exposure may darken the skin and delay it from lightening, at least for a while. Since you want this to fade as soon as possible, you're probably best off minimizing sun exposure until the skin heals.
This will take several weeks of gradual fading.
Unless you're taking Accutane, yhere's no special reason why you peeled this time, unless the waxing was done a little too aggressively. I would just share your experience with future waxers, so they'll be especially gentle.
But the most important thing to emphasize is that your lip will be normal again. Just wait it out.
Take care.
Dr. Rockoff