I bumped my car into a lamp post and it stopped completely while still in Drive. It was not a severe accident or anything, I merely scratched a little of the paint next to my left headlight. You know when you’re in Drive or Reverse and the car moves forward/backward still when you’re not pressing on the gas, well it seems to be moving a lot slower now after the accident. If I don’t press on the gas it would barely move at all. Did I do serious damage to the car?
Based on your description, you probably did not apply sufficient force via the accelerator pedal to damage your transmission. Consider that many car parks have concrete wheel stops to prevent drivers from entering the building while within the motor vehicle. These wheel stops do not damage motor vehicle transmissions, nor should the experience you've described.
Additionally, at low speeds, the automatic transmission has a fluid coupling between the engine and transmission known as a torque converter. It's easy to think of it as two tabletop fans pointing at each other. Instead of air flowing between them, the torque converter uses hydraulic fluid (automatic transmission fluid). When one "fan" turns by engine force, the fluid causes the second fan to turn, making the transmission drive the wheels. This mechanism serves, in this case, as a buffer to absorb the energy that would otherwise have been used to push down the lamp post. The fluid may have gotten a miniscule amount warmer, but would not damage the transmission.
It would still be a good idea to check your owner's manual about how to read the level of transmission fluid. Usually the vehicle must be warmed up for a short period of time and the transmission shifted through the gears (with the brake on) and returned to park. While running, the stick for the transmission is removed and the level checked to fall within the range marked on the stick. This is normal vehicle maintenance and is generally unrelated to your recent experience.
The description you've noted about the vehicle moving forward or backward when the pedal is not pressed is often called vehicle creep. It is an unfortunate side-effect of a torque converter and should not be a matter of great concern.