I had a mild sunburn on my face, can I get a superficial peel? Will it help with hyperpigmentation? (photo)

Thank you for the question. You should wait until fully healed from your sunburn before seeking any sort of peel, dermabrasion or laser therapy. A sunburn is a variable thickness burn through the outer layer of the skin. It is not uniform. The cells have been damaged, and many may die and peel off. You absolutely should wait til you are healed before undergoing any treatment. In the future, do your best to avoid excess UV light to your skin. It is very damaging over time, can lead to skin cancer, and contributes to premature aging, If outdoors, I recommend a facial moisturizer with SPF. 

You definitely want to let your skin heal first.  I would suggest strong sun protection or even better avoidance for at least 1 month, then doing the chemical peel. Moisturize, gentle cleansers, and no exfoliants or toner for the 1 month. See your dermatologist after 1 month to assess for the best people for your skin type and proper medical-grade skincare.