Will hyperpigmentation from glycolic acid peel go away? (photo)

I suggest seeking the advice of a cosmetic dermatologist or plastic surgeon and stop at home peels, they can do more harm than good.  In the meantime sunscreen and bleaching cream (hydroquinone or the like) would be useful.  I wish you the best of luck, Dr. Emer.

Post inflammatory hyper pigmentation is a real deal and can be very frustrating even for medical practitioners to deal with.  You need to consult with a board certified dermatologist.  There are dermatologists with an interest in managing post inflammatory hyper pigmentation but the truth is that any aesthetically focused dermatologist will be able to help you.

Dark skin is prone to post-inflammatory hyperpigmentation (PIH) ...Before you spend $$$ on lasers or specifically Clear + Brilliant, consider this regimen:
 recommend Melarase AM and Melarase PMto improve hyperpigmentation as well as Scler-X, a post-inflammatory hyperpigmentation relief complex. Scler-X is an oral supplement that is taken for 3-6 months or more for maintenance therapy.
Melarase AM in the morning. Melarase PM in the evening. Scler-X once daily. 
Also apply a wide spectrum high SPF 50+ sun block to prevent ongoing damage and PIH. I recommend Spectrase from Kare Skin. 
See link below.