Is this spot going to go away or is it perms and pigmentation issues? How should I go about treating it? (photos)

Do not do home peels.  While the products are available for sale on the internet, that does not mean you should do out, buy it and apply it to your skin.  This is your face we are talking about.  Extensive training is needed to apply and manage these agents to prevent harm.

You reacted more aggressively in one area.It is safe to use hydrocortisone cream as temporary method .This will decrease redness .Thr addicts of aloe Vera can also be soothing.

I would not recommend doing an at home peel again. There is too much risk of adverse effects without experience and there is no regulations on what you are buying in the products you purchase off the internet. It looks like you had a reaction to the peel you used. I would recommend you see a board certified dermatologist for proper care of the area so it heals appropriately and reduce the risk of long term effects.