Try to spray ball joints with WD-40 or similar product and see if squeek temporarily improves
Suspension squeaking in a Cavalier can be from suspension parts rubbing together. Check to insure that all of the bushings in the suspension are intact.
It could be bushings but, if you do not believe your mechanic maybe you should get a second opinion.
A arm bushings
Bushings are used in suspension parts, mainly.
There are bushings located underneath most of the vehicles. Bushings are rubber inserts that resist the shock of the driven surface. These rubber pieces are found on all the suspension components of the vehicle.
go to a mechanic
you'll need to put in new bushings
Ball joints control arm bushings shock absorbers springs, coil or leaf sway bar end links and bushings
There are bushings located underneath most of the vehicles. Bushings are rubber inserts that resist the shock of the driven surface. These rubber pieces are found on all the suspension components of the vehicle.
Check control arm bushings and other suspension parts specifically front swaybar bushings- these were a known problem for Chrysler- your dealer stocks them
There are 8 Bushings altogether for the subframe assembly on the intrepids. These kits range from 300.00-600.00. (and these are just the bushings) cheapest bushings I have come across are located at www.justforjeeps.com (not only jeep stuff here)
they are little rubber boots or grommets that go on bolts that hold two pieces of metal together and the rubber stops the metal from touching mainly you will find bushings in your suspension system