Check all of your fender and bumper bolts, check hood too tighten every thing down, plastic can make some squeaky noise up against metal, just check it out really. Could be a suspension problem, have springs inspected, best advice, get under neath it and start moving stuff, maybe have friends help, but "shake the front end" or "bounce" it up and down while a couple people listen for a squeak.
have the front swaybar links replaced
possibly hitting the front bumper
If the squeeling is coming from the tires, then the problem is most likely a misaligned front end. If the squealing is coming from the engine, then the problem would be in the power steering system.
Does Chevy cavalier have front shocks
Worn out ball joints, struts, lower control arm bushings, tie-rod ends, sway bar bushings, sway bar links, etc. Any one or more of these could do that. Sounds dangerous. Have the front end checked asap.
Are the front driving components(A-arms)from a 1993 Cavalier compatable with a 1990 Cavalier?
Front
front steering
1997 Chevrolet Cavalier LS Front and Rear Tires P195/65R15 1997 Chevrolet Cavalier Base Model Front and Rear Tires P195/70R14 1997 Chevrolet Cavalier Z24 Front and Rear Tires P205/55R16
it gets destroyed
Ball joints.
Sounds like your front-end bushings may need to be replaced. Without the proper tools you should consult a mechanic.