Strange noise and vibration on my Buick!

I have a 1991 Buick LeSabre custom, at the beginning of the winter, it would always work fine, heater would give out nice hot air, and it seemed to work fine, since we replaced the motor mounts and the spark plugs. About the end of December and beginning of January, the car started making this weird humming sound when I would start it and let it warm up a bit, and it sounds like metal against metal, but i was able to pin point the area where the sound was coming from, though cant really stick my head in there to see where its coming from, might go bald. Anyway, it appears to be coming from the driver view of sitting in the car, the far front right area of the car, near the battery. At first it would do it when I turned the heater or defroster on, but more recently the car has started to vibrate some and in one instance of speeding up to pass another car, when i reached the stop light at the end, the whole car had a huge vibration and it went back to normal. And now the car will make that either hollow or metal against metal sound will happen when i am ether letting the car warm up or just driving normally. I need help!!! Hopefully someone will be able to let me know what is wrong, oh and not to mention sounds like the belt is wet or something after a while, makes a squeeking sound.

Given the location you describe An alternator belt or alternator check would be step 1.