I heard this on a TV series, just don't know what it means:
But now I get this crazy idea, and I can't shake it.
The idiom to shake X is an informal way to say that you can't get rid of X.
So in this instance, the character in the TV show has an idea that they can't stop having or thinking about.
The classic example is when someone is being followed:
Meaning they can't get rid of the person following them (the tail).
Another frequent use is when talking about illness:
Meaning that they haven't been able to get over their cold.
I think the statement means that the person saying it has got a "crazy idea" and can't get it out of his/her head now. As in: