1990 lincoln town car squeak question

I drive a 1990 lincoln town car now when I first start my car up I hear a really obnoxious high pitch squeak after the car warms up and is idling normally the squeaking stops, but when I roll up the windows go from stop to start the squeaking comes back but stops a little after i start to accelerate I am not sure if this is the alternator or if one of my pullies has a bad barring could old coolant maybe also cause this problem? any tips/advice will be greatly appreciated