Hi,
I have a mountain bike which has an issue with the back wheel

I suppose you could call it vertical shaking. I have no idea how to fix it or if i need a replacement part.

The way it happened was my back tire got a puncture. While punctured the bike was cycled for a short distance, hitting some bumps.

When the back wheel is spun in a stationary position it (holding the back wheel in the air) there is no obvious bend in the axle or anything.

But it is possible to see the back wheel shaking!

Has anyone had this problem before or could give me some advice. I would rather not bring it to the bike shop and get charged.

Thanks