Freezing a foot from the ankle down to remove a foreign object such as a toothpick is not standard practice. In fact, most emergency room physicians, surgeons, and primary care physicians numb the area with lidocaine and then remove the tooth pick. A tetanus shot is given if the patient requires a booster.
I don’t know exactly what freezing solution you are referring to, but there is a serious risk of nerve, vascular, muscular and soft tissue damage from freezing the foot. Therefore, with the symptoms you are experiencing, you should be evaluated immediately by a qualified physician.