Noise from clutch

I just recently replaced my clutch in my car and have noticed a squealing kind of sound coming from the engine bay. When the clutch pedal is depressed the squealing sound goes away and when the pedal is released and not depressed the squealing sound starts again. This started to happen when the new clutch was installed and someone suggested it might have something to do with the tranny.

Another person said it might be a belt of something but that doesn't explain why it goes away when the pedal is depressed. I personally think it might be the throwout bearing or something related to the clutch. I also noticed that the sound will continue to make noise regardless when the clutch is in or out when the engine is warm and the sound is most noticable when the car is first started.

Yep, that is the clutch release bearing. Sounds like it was not lubricated when installed, which can often 'weld' itself onto your gearbox input shaft with the heat generated. The noise you are hearing is the bearing grating across the clutch fingers.
Best bet is to pull the whole lot out again and hope you have not stuffed anything to badly...
Good luck with it.