My teeth hurt after extraction but hurting on opposite side from extraction?

See your dentist. I'm sorry, but I do not know what you exactly mean by opposite side. Let say an upper right side tooth was removed. Do you mean the opposite side to mean the lower right tooth or to mean a left side tooth? See your dentist so they can determine your exact problem and help you.
Joint strain. It could be strain associated with the joint where you open and close your jaw. Have you called the surgeon who extracted the tooth. I would follow up with that doctor.