Blown head gasket or full motor replacement?

Lifters started clicking, had the oil changed out along with an additive added. Quieted it down for roughly 3 weeks, then clicking came back. I also noticed that the overflow to the radiator was boiling at times, and then other times completely empty, but the radiator was always fine ( I just put a new radiator and thermostat on as well ), and no water loss on the ground. Now the oil has turned a milky off white color, and of course the clicking is now continuous, however the car itself is running fine. I was told over the phone from a mechanic, that the motor most likely was ruined due to water getting up in the engine, this was why the oil had turned this color, and to replace the head gasket at this point for such an older car would mean much more work internally than the car's worth. Any opinions on this? I am about to just scrap it and call it a loss, but I am desperate for one last opinion before I make a move like this.