I waxed my upper lip and at first it was just red like normal.but now it's dark, very dry, and peeling.how long will it take to heal?what should i do

Depends: It depends on how deep the injury is and how dark your skin color is. Skin discoloration/darkening after an injury or inflammatory event can take as short as a week to as long as over a year to resolve. The worse the injury & the darker the skin, the higher the potential for prolonged discoloration. Keeping it protected from the sun and applying an ointment-based moisturizer (e.g. Vaseline) helps.

A couple of weeks: The facial area tends to heal fast and thus you will likely see marked improvement in about 2 weeks. But if the area has become infected, you will need treatment. I presume there has been no pus.