My 92 camry is overheating. on 1992 Toyota Camry

I replaced the radiator,thermostat,cooling sensors. I it possible for the water pump not to work if its not leaking out of the seal? I is my head gasket a goner? Bubbles blow back into my overflow as well.

Asked by for the 1992 Toyota Camry
If the bubbles start immediately upon starting engine , then , yes headgasket(s) are 'goners'. Depending on mileage and maint. history and general condition of engine, it may be 'that time'..........
When I first start the car it runs fine with no bubbles.After I run it for a few minutes to let the thermostat open it will get hot,then when I shut it off it bubbles back into the overflow bottle. I have no water in the oil,I replaced the temperature sensors,fan pump,radiator. The only thing I didn't do is replace the water pump. When I had it on the lift I didn't see any signs of leaking in the pump seal. Can the water pump fail inside in the accual gear that circulates the water in the pump? I didn't want to change the pump and timeing belt if the pump wouldn't be the problem. And yes the motor has over 100K on it but I always maintain it.
What you now described sounds like a faulty or incorrect t-stat. Is the bottom rad. hose getting hot BEFORE the bubbling starts? Is the correct mixture of coolant in it? Make sure your not diluting 'pre-mixed' coolant.