Firest everything freezes/now refrigerator will not stay running

Hello everyone. Thanks in advance for your help.
My old White Westinghouse Frost Free refrigerator I think has a bad temperature control. The first sign of a problem was when the freezer froze the ice cream so hard that I was tempted to get a chisel. Then I checked the refrigerator section and found that a half gallon of milk on the door was also partly frozen. I turned the dial back expecting the refrigerator to stop running. There was no click off. I turned it to off. It kept running. I unplugged it; plugged it in - keeps running.
After checking a bunch of posts I decided to tap the control unit. After three increasingly hard tap (set at off) it stops. Turn guage up. It starts. Down it stops. Cool. I think the problem is solved. I go in later. Not running. Turn it up. Not running. Tap it. It starts. Now when I turn the guage down it goes off. When I turn it up, nothing happens until I tap it.
If this unit is the problem can I just take it to a shop or do I have to get the information from the back of the frig?
Any ideas? Am I on the right track? And, yes, I know, buy a new one but that must be my last option.
Thanks again.
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