2002 Pontiac Aztec with 82000 miles

We have a 2002 Pontiac Aztec with 82000 we bought this last year used, everything worked well until winter hit. About three weeks ago we noticed it wasn't blowing any hot air in so we took it to a mechanic and they said the thermostat was stuck, so we had it replaced. A week after that it overheated and was blowing out cold air and then hot air, we took it back and they said there was air in the coolant line so they bled the air, two days later it did the same thing but worse, again they bled the air. It worked for about a week and now it's doing the same thing and very seldom do we get any heat. They are now leaning toward a blown head gasket but someone else said to have them check the water pump and see if there is any blockage. We need to get this resolved and would like any info ASAP as we need this vehicle to get around in, is our only vehicle. THANKS!