Screen side right and left shake

How often does this happen? How long does it do this for? After it happens, does it look normal again?

It sounds like your monitor is automatically "degaussing" (de-gowse-ing) -- this is a process which reduces built-up magnetic fields on the monitor which can affect how it looks over time. Usually, you'll hear a noise when it does it, and at the end of the process, usually a distinct "click" when it snaps back to regular operation.

Some monitors do this automatically when they are turned on, and some can be made to do it manually. I've not seen one that just does it at random times though.