If it’s coming from the hard disk, the head on the reader may have made contact with the drive. If you need data off the drive, take it to someone right away and power it down. Otherwise the drive platter and reader head will become too damaged to economically recover.
Typical desktop hard disks spin at around 7200rpm, 2.5″ laptop drives are typically slower, but regardless it will get damaged if left operating in that fashion as im sure you can imagine from the sound.
Ensure it is the drive before taking it in for data recovery or repair. Fans in a computer can get noisy as they go bad as well, so verify it is not that. Also, if it is less of a screeching and more of a buzzing, it could be a capacitor on your motherboard going bad.
When the drive moves to access data it will result in scratching on the platter and data corruption. if you are mechanically apt, you can use a (probably) tamper proof torx bit to open the drive, and gently lift the arm off the platter. It hovers a fraction of an inch above the drive platter, so don’t bend it up, ensure you keep it clean as possible, and reassemble.
There are a few videos on youtube that demonstrate how to do this, but keep in mind, if it is valuable data, do this at your own risk. Otherwise contact a professional.