^ It's absolutely this.
I always thought I played normal, but I needed this to be pointed out to me.
If no one has ever seen an e-sports player's physical movements, They have very light mice (under 75g), a mouse pad about 1m (3ft) long and move their whole arm left and right to turn their character 180 degrees while using just their wrist and flexing their fingers to fine tune the cursor onto the head for a headshot.
Here's how to improve:
First, start reducing your mouse sensitivity by 1.5 total percent each day. This is so the change is gradual enough that you can keep playing games like normal, but you'll have brought your sensitivity down to a more manageable level. This will also give your body time to build new muscles in your arm that you'll be using for holding your arm out and moving your mouse (you don't tend to use these muscles in anything else during the day. Don't try to skip to the end even if you're fit, because you'll over exert some specific muscles in your arms that you don't use because they're hidden under other muscles).
Once you're at the point where you comfortably need to move your mouse about 60cm (2ft) to perform a 180 in-game, you should start looking at aim-training. There are aim-training games that will teach you how to flick, track, etc... (If you're not exactly sure what these are, you will learn by watching some in-trainer tutorial videos) Aim-trainers are a lot more focused and intense specifically on aiming compared to regular games which means you build up specific skills in them much faster than regular games.
Spend about 10-15 minutes a day in the aim trainer right before playing your games. This will train you, but also warm you up so you're already playing well when you move to an actual game. The aim-trainer will track your performance and you'll notice it gradually trend upwards bit by bit for about 6 weeks.
By this point, you're probably better in some ways than the average player. But you're still going to get demolished by a few specific people you'll run into online.
To start facing those players, you'll be able to go into your aim-trainer (which has recorded all of your stats so far) and see which specific skills you need to practice.