Do you think having a parotidectomy could cause tmj?

It is possible: TMJ dysfunction is not an uncommon cause of intubation. The incidence of TMJ dysfunction following endotracheal intubation is reported to be 5%. If your parotidectomy was done under general anesthesia with intubation it could lead to joint strain or sprain.

Possible.: It might cause this but it should not last very long. The amount of time would vary but does not usually last longer than about two hours. The strain might last a short time but if it is longer than a month I would see an ENT for further clarification.

No, but: No, but pain in the area after parotid surgery can mimic TMJ pain.