If your bike actually has a freewheel, not a freehub, and was made after 1995 or so then you really don't want to spend much on it because it's probably a lowend bike.
If it really is a freewheel then the mechanic is kinda wrong in his assesment. Most shops would screw a new freewheel on for you for $40 or less parts and labor.
How many speeds? Disc brake type? Rim brake?