95 LHS overheating and no heat inside now

Ok I was having problems with getting heat from my 95 LHS so after some reading here I replaced the Thermostat and it didn't help so I had the heater core flushed. After the flush I has great heat and everything was working good. I went away for 2 weeks and the car wasn't used at all while I was gone. I get home and take the car into town so the wife could go shopping and I stayed in the car (with it running) while I waited for her (1 1/5 hours). Then I noticed the temp gauge was up to the last line and I could smell the coolant being released at the tank. I turned off the car for a while but when I start it and try to go home it keep overheating. I had lots of heat inside the car also. Anyway I left it for the night and the next day I started it and it took a long time for it to overheat but it did and now I have no heat inside the car either. I checked the hoses going into the heater core and one is hot, the other is cool. One more thing I noticed is the fans are not coming on either at the rad.
Could the heater core cause the overheating or is there something else I should look for before going there?
Ok I am pretty sure its the water pump now but does anyone know why the fans dont come on, maybe its the level of coolant being to loe to sence it?

I found something else out. If I rev the car up I get heat also but as soon as I lay off the gas the heat goes away. Sounds like it might be the water pump maybe?

Thanks

Sounds like your cooling system needs purged of air, there is a bleeder on the thermostat housing.

Also if the radiator fans are not working you need to find out why. (Open circuit, Fan motors are dead, bad relays, or fuse blown)

You may have a head gasket problem, and hot air is being pushed into the coolant system my LHS did the same where i would hit the gas and go and then the temp gauge goes up, my mechanic said it is the head gasket beginning to , its gonna cost 1900 to fix.

I purged the air from the system and it seems good now. I will know in a couples day of running it.
Thanks for the help.