I had a cold sore then it healed and turned white and now it won't tan. It's pretty big around my mouth. How can I get it back to normal?

Not much to do. When the skin is lighter after a problem at that location, it is called post-inflammatory hypopigmentation. That means the area lost some pigment-making cells, or the pigment-making cells are there but not making as much pigment. Thus, there is less (or very little) color there. The color returns in most cases and can take months to a year. If worried, one can see a Dermatologist after 1-2 months.