The squealing after starting up is USUALLY caused by the auxilliary belt skidding on the alternator pulley or the crankshaft pulley.
The reason is that right after starting up, especially on a cold day, the battery voltage will have dropped a volt or two, and the alternator tries very hard to re-charge the battery as hard as it can. If you have a 100 amp alternator (quite common these days) then at nearly 14 volts the WATTAGE the alternator is producing is 1,400 watts, and allowing for a little bit of losses, and that every 748 watts needs one horsepower, then the auxilliary belt is needing to feed well over 2 bhp into the alternator alone. IOt is quite a drag, and as the belt is hard and stiff from being stone cold, it slips - and squeals.
It is not good for belts to let them squeal.
If your battery is a bit duff, or too small an amperage, the problem gets worse.
I used to spray a little WD40 on old Vee-belts to stop the squealing, which may work on new flat poly-vee belts too. I am told the slight trace of oil takes the shine OFF the belt and also makes it a little more sticky, so it drives better.
Just don't be tempted to over-tighten the belt as it will break up and snap.
CharlesY