Can tight painful bear hugs cause ant spinal damage? Spine hurts after receiving one several hours ago. Very tight hug, made me yell at the time.

No. It is unlikely there could be serious injury to the spinal column itself by the mechanism of getting a "bear hug". That being said, other injuries could occur including injury to the ribs or abdomen. Don't hesitate to be seen if you think you have sustained a serious injury.