Toilets can make all kinds of sounds when they malfunction, including hissing, gurgling and thumping. Screaming may be more annoying than most sounds, but it doesn't necessarily signify a more serious problem. It usually comes from an older toilet with a ballcock fill mechanism. As the tank fills, the float arm partially closes the valve, and vibrations in the pipes make the screaming sound as water tries to get through the smaller opening. There isn't an easy way to repair old ballcock valves. The best strategy is to replace yours with one that stays open until the tank is full.
Turn off the water supply to the toilet and flush it. Hold the handle down until the tank has emptied as much as it can.
Sponge out the remaining water in the tank and transfer it to a bucket. When you have got as much water out as you can, disconnect the water supply hose by unscrewing the nut from the fill valve inlet on bottom of the tank. Place the bucket under the inlet to catch any water that may still remain in the tank.
Disconnect the rubber overflow tube from the overflow pipe and unscrew the nut under the tank that holds it using slip-lock pliers. When you have removed the nut, put the bucket under the valve and lift it out of the tank.
Place a new fill valve that has a float cup encircling the body of the valve in the hole in the bottom of the tank. Adjust the height of the valve so the critical fill mark on the valve is 1 inch above the overflow tube. Make sure the valve is positioned so that the float cup can rise and fall without hitting the sides of the tank or any other obstructions.
Screw on the nut from underneath the tank to hold the valve and seal the opening. Tighten it with slip-lock pliers. Clip the overflow tube connected to the new valve to the overflow pipe in the tank.
Screw the water supply hose to the new fill valve and tighten the nut by hand. Turn on the water and check for leaks while the tank is filling. Adjust the water level by moving the adjustment clip up or down on the fill valve. The tank should stop filling when the water level is about an inch below the opening of the overflow pipe. Flush the toilet once to make sure the tank refills to the correct level.
Replace the valve with a new ballcock valve if you prefer. Be sure to buy one that doesn't close partially as the tank fills. The vibrations from a partially closed ballcock can be transmitted through the pipes, causing screaming or whistling sounds at locations far from the problem toilet.