If the bike is only a year old, you probably have a freehub rather than a freewheel. What happens is your cassette (the rear 7-gear cluster) is attached to the freehub which allows the gears backwards motion (relative to the wheel) so you can coast.
Since the mechanic reccommended a replacement, I'm guessing that your freehub is cracked. If this is indeed the case, there's really not much you can do to fix it other than pay the 25 bucks for a replacement.