I agree with powers2b. Sounds like you have a bottom-bracket lockring on there. BB lockring and freewheel threading is often the same.

Yes, swap sides. A fixed cog on the free side using a BB lockring is not a good solution (although I've done it using a regular FW hub - but I also used two brakes and did not try to brake with the cranks). Not only do you need a freewheel remover tool, you need a track hub lockring