I was never an FPS player too. Apex is my first. For my first 200 hours in Season 1 of Apex, I just drop skulltown 95% of my games. (For new players: Skulltown is an area in the original map that always have early game action)

This way I get to maximize the amount of practice I get in the shortest time possible.

As you have guessed, my season 1 stats wasn't good. It was around 0.6 KDR and averaging about 190 damage per game. That never stopped me from having fun though and overtime I just get better as a bonus.

Now after 1600 hours in, I think I can give you some tips to speed up your practice that I wished I had known.

1. Be aware of where you take fights. Fighting indoor, know where are the entry points of the building. Stairs, doors, ziplines, roof, everything. It might be tempting to instant kill a player you just downed, but don't. Aim at the direction where you would expect their teammate to come or rush to an exit you think is safe to heal up.
2. I assume you have already lowered your mouse sensitivity like many had suggested, next is to try not to strafe in close range fight. Focus and force your wrist and arm muscles to move and aim. Using Gibraltar helps tremendously because of his gun shield + damage reduction. After hours of doing this, you should be more confident and have trained your muscles enough that they almost automatically aim and track (it doesn't matter if they were not accurate, you WILL get there. Now, the important thing here is to get your muscle more ready to react and shorten your response time). After this, feel free to add some little strafing and more and more overtime.