Artificial intelligent assistant

How can I fix my back wheel's wobbling? On my single speed bike--a POS J Fixie Cafe CF from BikesDirect--has an issue with its back wheel. The wheel wobbles 1cm back and forth when pulled/pushed from side to side. The freewheel has been making noises since the day I got it. The noises are KLINK! KLONK! every time I pedal. I believe that this is due to a bit of a warp on the frame that makes the tire asymmetrical to the frame. Basically the left seat stay is slightly larger than the right one. (The lesson here is not to buy from BikesDirect, but go to a LBS.) Anyway, what can I do to fix this? Do I need to get a whole new back hub? Freewheel?

What I think you are saying is that when you stand beside the bike and push it side-to-side you can see the wheel wobble.

That sounds to me like the bearings in the rear hub need to be adjusted. They don't need to be far out for it to cause significant movement at the rim.

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