After the car overheated, now the impala is shaking while ideling.

Have oreilys scan it and let us know the error code

No pushrods in your overhead cam engine. It's "shaking" because you have an engine misfire. as above posted suggested, get the trouble codes scanned so you can get an idea of why it's misfiring.

P0300 multiple cylinder misfire and it said it might be one of the distributor coils