Hi, thanks for posting your query.
You seem to have developed post inflammatory hypo pigmentation secondary to chelitis of lips.
The following treatment may help:
based cream like fluticasone
in the morning.
-tacrolimus cream at night.
-keep your lips moist with a lip balm.
-avoid using other lip cosmetics for the time being.
You may start this treatment under a dermatologist's guidance.
Hope this helps you.