Let me see if I understand. Compression test front to rear is 85 120 160 160. That almost certainly says blown head gasket and or warped or cracked head. Low compression on adjacent cylinders indicates this. It does not indicate worn rings. Have you checked for coolant in oil and/or oil in coolant. These are also signs of head gasket problem. Did your mechanic discuss the compression test results with you? Did he say it was rings? Same mechanic that left off the sock?

Replacing the head gaskt is an awful lot cheaper than rings. If the head is cracked oe warped too badly good used or rebuilt heads are easy to find. I would not entrust such work to a mechanic that would leave off his socks.