How Do I Get Rid of Depliatory Burn Marks from my Cheeks and Chin?

First and foremost, you need to be examined by qualified health care professional.  There are many different possibilities for the pigment or color changes you see in your skin, but very likely you have some type of post inflammatory induced pigment following your procedure.  This condition can often be treated successfully with topical creams, in particular those with hydroquinone if you are not sensitive to hydroquinone.  There are also in office treatments, often in the form of chemical peels that can compliment the positive effects of product you use at home.  A more aggressive approach if contraindications are ruled out and clinical evaluation favors include IPL, but I would only do so if you are a skin type 3 or lower.  Some consideration may be given as well to a fractional, non ablative laser again depending on clinical evaluation. 

Excess Pigmentation and Texture Changes After Depilatory Treatment may be what you are having. You could benefit from bleaching creams and certain 'bleaching' peels that will significantly lighten the area. The use of these bleaching treatments may be alternated with sessions of microdermabrasion for enhanced results.

It sounds like you have post-inflammatory hyperpigmentation after irritant contact dermatitis from a depilatory.  Consult with a board-certified dermatologist to see if a prescription strength hydroquione product will help.  Good luck!