How long will it take for post inflammation Hyperpigmentation to fade?

It is difficult for me to provide a formal assessment without seeing you as a patient in my clinic, but in general, treating PIH requires a combination approach of lasers, microneedling, chemical peels, and a good cosmeceutical regimen. It is important to ensure that your inflammation has subsided before having any additional treatments. I strongly recommend scheduling a consultation with a board-certified cosmetic dermatologist who is an expert in facial rejuvenation. They will help provide you a formal assessment that takes your history into account, and will recommend the best treatment plan moving forward. A glycolic peel in 2 weeks may be too soon. Consult an expert. 

Hyperpigmentation from any type needs a combination approach of peels like cosmelan,  lasers like clear and brilliant and aerolase or laser genesis, radiofrequency like venus viva, and constant skin care and sun protection.  Bimontly facials with silk peel dermalinfusion is essential to hydrate, exfoliate and infuse vitamins and antioxidants into the skin.  If you have acne you can do additional treatments and peels to get more improvement.  I suggest a formal consultation with an expert in lasers and peels. Best, Dr. Emer.

Thank you for your question and posting pictures.  It looks and sounds like you might have Post Inflammatory Hyperpigmentation (PIH).  PicoSure Flat or FOCUS lens treatments should be able to take care of it easily with almost no risk.
FOCUS lens treatments have the extra benefit of reducing the underlying scar tissue.  This is one of our go to treatments for patients older than 40 and worried about the signs of aging.  This laser is safe for all skin types.  Start with sunscreen every day!  Once you have treated your hyperpigmentation to your satisfaction, you will probably need a follow treatment every 6 to 12 months depending your level of re-pigmentation.  Best of luck.