What concerns me is that when I pick the bike up by the seat and spin the rear wheel forward, there is tension. The wheel will roll a couple of revolutions and stop and the pedals spin as if it was a fixed gear. When I attempt to spin the wheel backwards, it will act as if the chain is binding.

I put another wheel on today and everything was fine. The shop was right. It is in the freewheel. I just don't know why since the wheels are about 6 months old.