1 Month Post TCA 40% Peel on Face and Still a Little Swollen and Now I Am Getting Darker Around my Mouth and on Cheeks?

The pinkness usually goes away and the fact that it is persistent means you probably had a significantly deep peel. The brown discoloration is more of a problem. It is important to pre-treat with some prescription creams first and use the same products when your plastic surgeon or dermatologist allows you to use it again. This is to prevent brown spots following a TCA or any other peel, laser or deep dermabrasion procedure. This is  called post inflammatory hyperpigmentation. The inflammation part is a normal part of the healing process but unfortunately you are sensitive to the sun which is what causes it. Ideally your doctor would have pre-treated your skin some weeks before your treatment with Retin A, 4% hydroquinone, and a strong SPF sunscreen and/or other agents to prevent this from happening. As soon as you are given permission you would again start these products plus perhaps Kogic acid and use them for some time. Once they are established it is more difficult to get rid of. The same treatment can be done again but this time use products recommended by your doctor before and after. If these were not suggested you might want to seek another plastic surgeon or dermatologist for a secondary consultation.

Recommend that you start a medical grade skin care  to stabilize the pigment layer of the skin, then multiple skin peels or if you are fair skin fractional CO2 laser resurfacing. by a good plastic surgeon. It will be a long process and multiple treatments to get where you want.

It sounds like you may be experiencing rebound hyperpigmentation.  Was your skin "pretreated" prior to your peel?  Ask your dermatologist about this because there are products you can use to help with this.