The thing (that you pretty much mentioned already) is that to have a good experience, you have to play better than you can. But, improvement is almost disconnected from enjoyment, because it supposes to be hard work. Before realizing the method of practice, you have to set your mental to an appropriate level.
When I find myself dying a lot, I figure out what was my playstyle last rounds. And if it was aggressive, I play passive and vice versa. You have to spectate other players and analyze what they do and learn from that. If you think that there is nothing to learn from that, then you need to watch some high-rank players on twitch, or, which is even better, find someone smurfing, so you can pick up what is the difference between his playstyle and yours besides aim.
To practice aim, aim lab, and other trainers are pointless. You have to play the actual game and grind it hard, a minimum of 5-7 matches a day and going up to 10. Mix it up with deathmatches, and set goals for yourself. For instance: I play 1 ranked match, then I play 1-3 deathmatches until I take 1-3 places or go above 30-35 frags. If I can not get this goal, I go and shoot bots (30 seconds HARD+ARMOR) until I reach a consistent 18-22 hits or 30. Then I go back to DM and check if my aim and movement are on point, then go to the next ranked match. Played the next match poorly (below 15 frags) - repeat DM+range routine.
To practice aim, the first thing you need to realize is what is the aim. It consists of a lot of features. It is not just raw mouse movement, it is not just a crosshair placement, and it is not just flicking or tracking. The aim is a prediction-reaction thing based more on your experience plus the way you move, counter-strafe, and counter your enemy movement.
When you play a lot you start doing things automatically, but before that, you need to develop good habits over your bad ones, and you need to be aware of your bad habits to make a difference.
For instance, when I learn how to aim, I noticed that as soon as I peek at an enemy in a direct 1v1, he strafes slightly away. Then I think, was that to counter my crosshair placement? Yes! But I was wrong because the strafe helps him to adjust his aim at first but for me, it also makes a hard time to place my crosshair on his head. Then I started doing the same by myself, and it made a lot of difference.
And there are a lot of these little things that you won't be able to notice without super-hard dedication. If the fun stays in first place for you - you won't be able to improve. Because improvement is 100% pain. You need to go through that and keep your mind clear to see the little things that you don't notice because of emotions and wrong priorities.
When you die - analyze, say: "What could I have done better" - that is your best coach. And as soon you have no answer to that question, that should be an alarm for you, meaning that you are tired and pretty much wasting time not learning. Be hard on yourself, but never tilt. Use every moment of the game to learn, that will prevent you from tilting. Sometimes your enemies are just stronger, and you need to be aware of that to not tilt. Give yourself time to improve, but don't waste it.
