He is probably right. Do know that sway bar bushings can squeek too,and may
be the problem.Upper control arm bushing is more expensive than difficult.
You need 4 bushings @ $15-to about $30 each. They are presssed out, then
in.A tack weld on each prevents movement.You need a front end alignment
also.About $400 I would say.

This sway bar has 2 bushings. An inner and outter bushing.You can squirt
something like WD40 on them to check.

If this is the problem, swap the left inner bushing for the right inner
bushings and coat all bushings with anti sieze compound.