Sounds like your radiator is really plugged up.Look in the end with the cap off. Check the tube openings inside,if they are covered with a white crusty looking crud, then it is plugged.
To confirm the pluggage, if the engine is good and warm,stop the car and open the hood, if the radiator feels cold at the bottom and kinda warmer toward the top , it is plugged,it should be pretty warm to the touch if the water is flowing through it well. No need to guess, just feel it to see.A cold radiator is a plugged radiator
BTW, if the AC was turned on, the fan may not kick on as it comes on according to head pressure, which will be real low on cold days.That is why it didnt come on.