My Face is Having Hyperpigmentation After Chemical Peel. Could my Face Healed by Itself? How Long Does It Takes? (photo)

i got my face peeled 9 months ago , I was having really bad hyperpigmentation. Now , the hyperpigmentation is lighten but still can be seen under bright light. I'm not having any medication even sun screen. I wash my face twice a day with cetaphyl. I have a bad oily face. My question is could my hyperpigmentation healed / faded as it used to be? because my face now is turning like a zebra. and How long does it takes to heal without having any medication ? the contrast is at my mandible (lower jaw