Cars break down all the time. Your mechanic is not psychic. When they DO find things for you to worry about people accuse them of trying to sell them unneeded parts. You can't have it both ways.

I'm not clear on what you mean by "tug". To me that implies the car is trying to pull to the left or right and you have to pull back on the steering wheel to keep it going straight. That is an alignment, brake, or tire problem. If you mean it was losing power, that is one of the final indications of an overheating engine. You should have seen a rising temperature gauge or a temperature warning light on the dash. The place to start now is by having the engine checked for a leaking cylinder head gasket. An overheated engine can cause a cylinder head to warp and let the gasket leak, and a leaking gasket can cause overheating. It can be hard to figure out which happened first. At the mileage you listed a corroded and leaking head gasket is nothing abnormal on any car. There could also be some other relatively minor coolant leak that caused the overheating. Radiator and heater hoses rot from the inside and will look good on the outside. Hose clamps work loose or rust off. Hoses develop pinhole leaks.