Will my Jessner's Peel reaction go away? (photo)

  I agree with the other doctors that you could be having a postinflammatory hyperpigmentation reaction.  In addition to the sunscreens, and the hydroquinone previously suggested, I would advise daily use of Retin-A.  Fortunately, you should see considerable improvement on this regimen soon.

Your initial reaction of turning dark brown and peeling was completely normal.  Unfortunately I have to agree with everyone else and it sounds like you have PIH (Post Inflam Pigment).  Most of the time this will fade on it's own, but it can take 6-12 months.  If you return to the place where the peel was performed they should work with you to lighten the pigment more quickly through light treatments such as: vit c enzyme masks or other products that will calm and lightly exfoliate the skin.  Retinol and hydroquinone are key ingredients to help the darker pigment fade faster, but you should use a topical steriod at first to help with the inflammation.  Please have patience and faith that in time it will get better.  I strongly discourage you trying to self-medicate this area, as it is already sensitive and you don't want to furrther exacerbate the dark pigment. 

Call the doctor  who did the procedure.  They have an obligation to be knowledgeable and available to help you recover from procedures that they perform on you.

Your best bet is to use moisturizers 4-6 x/day. Sun screen usage EVERY day is mandatory. It may be advisable to  avoid doing the peel around your mouth in the future

The good news is that it is typical for the skin to turn brown with a Jessner Peel.  However the brown should flake off and go away.  It sounds like you may have post inflammatory Hyperpigmentation.  This happens when your skin has been damaged and causes new pigment cells to rapidly multiply.  I would suggest getting on an anti inflammatory and some hydroquinone (that controls the pigment).  I would then suggest refraining from getting another peel for a while.