Discoloration after CoolSculpting not common.
CoolSculpting works by slowly chilling the tissue to just above freezing and then maintaining that temperature fo r one to two hours (depending on the applicator used). If the skin is very sensitive to irritation it is possible to see some pigment at about 3 to 6 weeks that could last for several months. This is called post inflammatory hyperpigmentation (PIH). In the many hundreds of patients of all skin types that we have treated I have not seen this.
Another issue that may be interpreted as pigment is simply due to shadows. I have found that in inner thigh area can have the illusion of darkness even before CoolSculpting due to the draping of the skin when standing upright. This is especially true when skin laxity is present.
Skin discoloration post coolsculpting
I have not seen skin discoloration that has presented itself this long post treatment. While extremely rare and for those with extremely sensitive skin, Post inflammatory hyperpigmentation (PIH) is possible but should present itself more quickly. Consult with your treating physician and a dermatologist to understand what could be occurring. It may be unrelated to the coolsculpting treatment.
Coolsculpting is a great non-invasive fat reducing procedure. I have not seen any discoloration after the procedure. Was it red originally? If you have some post-inflammatory pigmentation it should resolve in time. I suggest you consult a board certified dermatologist for another opinion if this is of concern for you.