Car squealing when I turn in, take off, accelerate etc.

Most of the time when I start my car it gives of a loud squealing sound. The car will also do it when I accelerate or first leave from a stop sign or stoplight while have the AC on. Once I turn the AC off the car will stop squealing and move a lot faster. I have also noticed it doing when I turn at times but those times I believe the AC was on. The serpentine belt was replaced last year. Today a mechanic came out and said that the belt was fine and that it was tightened enough. He believes the alternators bearings are going bad which is causing the squealing that having the AC on was causing to much on it, like over working. Should I replace the alternator or is their another issue that could be causing This? I have used belt dressing before and it was only a temporary solution. I also have noticed sometimes when I first start the car and try to drive off immediately the car kind of stalls for a second and then goes.