1992 Acura Integra thermostat/heating problem

Ok here goes and I really dont know where to start but I drive about 200 miles a night for my job and its in the teens here and freezing me to death with no heater. About a month ago my car started over heating so I bought I new thermostat 180 degree put it in. Over heating stopped. Then recently it started back but alot worse almost in the red. Flushed the radiator clean fluid was put in and a new thermostat again a 180 degree since thats all the parts store had. Well its overheating worse after that. The upper radiator hose was hot and the bottom one cold when we stopped while it was overheating. I know the fan works we had it straight wired to work all the time since the last episode of overheating. Also when I stop at a paperbox the heat would feel like air conditioning and the car would cool down. When driving away from the box and accelerating the car would overheat and the heat would get extremely hot. We couldnt figure it out since the thermostat worked outside of the car in the boiling water test we did but when it got into the car its like it just didnt work. So we took the thermostat out since I drive alot at work I couldnt have the car overheating anymore. Now the car wont get off of the cold idle to run without running really rough on the motor. It sounds horrible and im terrified the motor will go soon if I keep driving it with it being this cold. When I stop for about 10 minutes it will warm up and then cool back off imediately when I take off again and accelerate. We unhooked the fan completely thinking it was making it run even colder but it didnt have anything to do with the car warming up. Please any advice would help we are in serious need.