There are several things that can cause your 2005 Chevrolet Malibu to run rough. The fuel injectors may need to be cleaned. The air filter may need to be replaced.
did you gap your plugs right!!
it sounds like your timing may be off
Some parts stores will scan your vehicle for free. Advance auto for one.
This happens sometimes when there are teeth missing on the fly wheel
Carburator problems -- dirty gas -- water in gas
Your car is not getting enough fuel if it hesitates to take off and shakes. The fuel filter might be plugged or you might have the wrong gas in your tank.
bad shocks
sounds like you have a leaky intake manifold
It usually affects the hand , and it shakes , very badly.but sometimes it affects the other hand as well .
Delinquency, at my high school, was skipping class and getting burgers and shakes at Cook Out.
Shakes and shimmies? Try getting your tires balanced and your front end aligned. That might help.
Possible head/headgasket failure.