A spot that comes on that quick isn't likely to be anything sun-related or dangerous. The variation in color during the day probably just reflects how much moisture is in the lip. Could it be persisting because you lick or bite it, consciously or otherwise?
I would ignore it for another couple of months, and leave it alone as much as possible. If it's still there in, say, two months, show a doctor.
Best.
Dr. Rockoff