Do i need a new alternator?

I just replaced the battery on a 1996 Pontiac Grand Am, 2.4L. Now, the guy at autozone tested the alternator and said that it was giving to many amps or something off, and that was a sign of a bad alternator. I had it tested because sometimes when I sart the car up, and I turn the heat up on hi and have the lights on, the car starts to vibrate real bad and the engine starts to make a squeling noise. And when I sart the engine up the battery light comes on too. What could be wrong or what is wrong? Is it the alternator?

Yes, the internal voltage regulator is bad and the alternator is burning itself out. Buy a new or reman unit and it should be fine. Make sure the connections are clean when you reinstall the new alternator and check the battery connections to insure they are clean and free of corrosion.