Weird screeching noise
 

So today I noticed my car is making a weird screeching noise when it's cold. Everything would start normally, but when I hit the clutch pedal, the car would make a loud screeching/whistling noise. The AC was off. When I release the clutch pedal, the noise would stop. The noise would go away after I drove it for a while and warming up the engine.

My car is around 186k right now. I am planning to change the transmission fluid this weekend and also changing my engine oil. I don't want to change the transmission fluid this weekend if I have to open up the transmission to get work done on it.

Can you guys help me diagnose this problem?

Thanks,
Son