Is this a normal reaction to an at-home chemical peel? (Photo)

More information is needed.  What kind of peel did you do at home?  Was this product purchased from a verified source?  In-home peeling agents are very risky.  There are a lot of products being sold on the internet that can leave you with harmful side effects like what have in the picture you posted.  Peeling products should be administered by a professional.  For darker skin types, I also recommend that the area be prepped with a skin care product that reduces the chances of hyperpigmentation for 2-4 weeks prior to any peel.  I would go to a dermatologist or other medical professional and have them look at the area.  They can prescribe a product with hydroquinone  or another lightening agent to help with the darkening.