Ref: Fan Belt noise issue
Fan belt screeching in morning and gets better when engine warms up is thermodynamics of metallic pulleys. Pulleys expand and grip the belt.
Reason is the belt is loose and it is pretty much useless now after making all the noise coz if you get it tightened properly it will snap at any time.
I think you have changed the alternator and naturally alongwith it the pulley of your original alternator got changed.
Most of the second hand alternators available have worn out pulleys with sharp grooves, they tear the belt apart in no time no matter "bando" or "Sumitomo"
Solution:
Check the alternator pulley for sharp edges , if original one is available just replace it.
Get a new belt of the above mentioned brands and tighten it properly while the engine is cold.