If your cog keeps slipping when you try to backpedal (brake) you may have smoked the threads. Have you noticed any aluminum shavings by the cog??
If this is the case, the fixed side of the hub side is probably messed up. You can take it to a shop and see what they have to say.
I would highly recommend you get a bike maintence book or get friendly with your LBS. Fixed gear bikes are meant to be low maintenence but when you have a problem you should address it immediately. This will save you alot of money!
Do you have any bike tools? You will need a headset wrench (thin wrench that fits in the top cup of the headset), cone wrenchs (to tighten up the the cone on the rear axle), a chain whip and hooked ring wrench for the cog.