Do I have a chemical burn from jessners peel? How should I treat? (photos)

I would always encourage you to see your provider to discuss questions especially post-peel care. A jessner's peel is an epidermal peel and can only really cause some exfoliation of the skin. It doesn't penetrate into the dermis. Loop back in with your MD to discuss post-peel care and your concerns. 

I recommend following up with a cosmetic dermatologist for after care following your peel. I recommend silicone gel with growth factors to promote healing. Hyperpigmentation can be improved with a combination of lasers, Aerolase, microneedling/prp, skin lightening, peels, and skin care. Sun protection is essential. See an expert. Best, Dr. Emer

Once the acute burn is treated appropriately ...For uneven skin pigmentation I also recommend a skin regimen prior to to prepare the skin for the peel. 
Melarase AM cream is great to reduce hyperpigmentation and to correct uneven skin pigmentation.
 I also recommend Pigmentation Correction Complex to reduce hyperpigmentation of the skin.
Also avoid sun exposure to prevent inflammation and skin burn injury for at least 4 weeks. Spectrase is highly effective. 
Best
H Karamanoukian MD FACS

I would recommend you follow up with your provider or a Dermatologist to review post peel care for optimal healing. A dermatologist will be able to provide you with the appropriate prescription creams to aid in the healing process as well as any post inflammatory hyper pigmentation that may result. 

Hello, based on your photos, it appears to me that you will need a topical therapy plan to expedite healing. The combination we use includes Alastin Skin Regenerating Nectar, a prescription steroid ointment, and hydroquinone. Of course, I highly advise to follow up in person for the best topical healing plan for you. Please avoid picking off peeling patches. I think if you follow up with your treating physician and do your aftercare, your skin will do well in the long run! Best to you.