My tv (motorola 21t16) does not have any shields for the tubes. There are two tube sockets that have a "finger" connected to the chassis that sit up against a tube. Does this automatically mean there should be a shield in place?

Yes, you need to have shields on those tubes. I'm guessing that they are on the tuner.... Look closely for other tube sockets that have a raised flange around them. They take shields as well....