There is a bleaching cream you can get from a dermatologist that is helpful to lighten the scar if you have light colored skin. You might be able to ask the doctor about that. It takes a couple of weeks before you notice the ligthening but it does work.
I had my very first outbreak in the middle of January. I was fortunate enough to only get one cold sore but it was a fighter and stayed on my upper lip for almost three weeks. When the scab finally came off, I was mortified to see that it left discoloration on my lip -- a dark brown scar (from the site of the cold sore) and some light pinkish spots. I immediately applied aloe vera gel, and within the week my lip's color was slowly returning to normal. I suggest using pure aloe vera gel straight from the plant and apply it to the scar every four hours. Make sure to massage it gently to stimulate the blood, though. A good 20 seconds or so would do.
The light pinkish spots are completely gone. The dark scar is turning to its original color, but I haven't been as diligent as I was the first time I treated my scars so the healing time is slower now. :P Also, make sure to wear lipbalm with SPF protection when you go out to prevent undoing all the hard work.
Good luck to everyone~
Try what Fat_Dave posted. Aloe Vera gel should help