Engine misfire? Engine shaking

Do you have a check engine light and when was last tune-up??

https://www.2carpros.com/articles/engine-misfires-or-runs-rough

1.Defective spark plugs
2.Inadequate spark/coil,defective spark plug wire.
3.Lack of compression
4.False air leakage.
5.Faulty fuel injectors.
6.Insufficient fuel pressure.
7.Contaminated fuel.
8.EGR valve that is leaking.
9.Oxygen sensors.
10.Throttle position sensor.
11.Manifold absolute pressure sensor
12.Mass Airflow Sensor
13.Idle air control valve

Note: If it doesn't apply disregard it-

Sounds like a misfire.

May be not getting enough fuel to the engine due to a weak fuel pump and plugged filter-shck fuel pressure to see if it is in spec.

Check for good spark to each cylinder, may be a bad plug, wire or coil. Is where I would start.

Does your car shake the same when cold as when it reaches operating temperature?

I assume it gets worse when you put it into gear? Does it go away if you rev up the engine in park or neutral?

Does it almost stall the motor?

My first thoughts are a dirty throttle body and intake, dirty injectors, dirty or clogged fuel filter.

Other than that, your motor mounts could be worn out.
Depending on the car and the driver, mounts in different stages of failure can; cause vibration at idle, allow the motor and transmission to move excessively and lead to other parts being damaged.

Internal and external bablancers are always a suspect as well becasue they will be at a ower harmonic at idle giving the most imbalance and decrease as motor speed increases. Don't ignore this because even though you don't feel the higher harmonics, a failed balancer/damper, will cause engine damage.

Relating back to the first thought, engine performance. You could have internal engine problems such as uneven compression, which you can either find links for help in finding a certified and reputable repair facility near you in this link.

From here I would think the best place to start would be a few things that are general service items as to eliminate them as the source of the problem.

Try replacing the following;

air filter
spark plugs and spark plug wires, especially if the wires have never been replaced
I cannot recall if your car has a distributor, if so replace the cap and rotor as well
Run a can, 2 if you never have, of injector cleaner. I suggest BG44K which you will probably have to go to a gas station or car dealership to get.
I believe your car has a, "In the tank filter", so it cannot be serviced. However double check this, when you are purchasing your parts as a reputable parts store will be able to tell you. If it is servicable, replace it as well.
Finally, an O2 sensor for good measure.

Use the links available on this site as they will be helpful. There are great video and text walk-throughs of performing general maintenance.

Detailed information specific to your vehicle is not readily available on-line. That is why I mentioned checking on the type of fuel filter through a reputable parts store. This is information found in service manuals which require a fee to use.

A dealership will give you the information if you purchase your parts there, but they can be more expensive. You might still ask if you get your BG44K at a dealership. Dealerships will be the best source for information as they use the factory Parts/Service manuals for reference.
The link to the on-line Mitchell manual is very much worth the cost as you will have a Dealer Level service manual for any vehicle you have or will work on. Service manuals from dealers are the only truly comprehensive source for all car specs and maintenance information, but they cost at least $100 or more. You can get a Haynes manual from an auto parts store for around $30, but they are very generic in that they cover several years and models with much less information.

Let me know how everything goes and I wll check back soon.

Is the check engine light staying on? Have you checked the catalytic converter?

Let me know.
Joe