AC/Heat Issue for 98 Ford Contour

I own a 98 Ford Contour with 135000 miles on it. Over the past few months the heat and air had went spotty. The car would make a loud shriek on a cold start when the heat or air was turned on.The shriek usually lasts until I would get out of the driveway and the end of the street. If I turn the air off during mid-shriek and then turn it back on, the shriek would not return.Then one day, after the car started and the shriek quickly came and went, the air did not come on after. When the car is moving a little bit of cool air is pushed out but the fan isn’t on and stops when the car is at an idle or stopped. The shriek continues. I tried it with the heater and it does the same thing. Any ideas? It gets hot down here in the south in the summer.