1990 Mitsubishi Eclipse Overheating

I have a 1990 mitsubishi eclipse gs non turbo 2.0L and it is running hot, I replaced all the radiator hoses and heater hoses, the thermostat, and the radiator cap. And I flushed out the radiator. And changed the antifreeze multiple times, every now and again the car will make a high screeching noise but goes away no longer than 30 secs. I purchased a waterpump, but it's going to cost a lot to get it replaced, and I just wanted to see if there are any other possible problems that would make it overheat? The car overheats at idle, it runs fine when first started, when it warms up to the normal running temp it runs rough and the rpms go up and down then it quickly overheats. What could be the problem?