I think the most important thing to focus on improving is your aim. I have terrible teamwork (I focus 90% on killing people and 10% on the objective) but since my aim is above average I can break 3000 SR.
Make sure you're using a low sens and no acceleration etc.
I think my aim's generally OK.
A couple months ago I lowered sens from ~12 to 7.5, and since then have been doing better.
With McCree I can 1-v-1 most opponents (overbuff shows 50% accuracy, but I don't trust that site very much), I can shoot pharah out the sky as Mei, generally keep my scoped and unscoped accuracy over 60% when playing Ana etc. I can't think of many situations where I thought "one more shot on target and I would have got them" except playing as zarya with her annoyingly intermittent beam.
It's also no problem getting multiple medals (not uncommon to get 4 golds and a bronze/silver with Soldier).
The bigger problem is definitely in my teamwork - if I can get behind their lines and kill both healers, but don't manage to sync it so my team pushes, I will easily get golds but I'm not realistically improving the chances of our team's winning. I'm thinking of challenging myself to stick with the tanks, or choose another player and follow them, supporting their plays rather than making my own, see how that goes. I also need to learn some characters better.
First ever comp game as reaper the other day, when someone recommended I swap off McCree on Ilios Well. I got a 5-player death blossom kill (achievement and spray!) and PotG, but as I only have 10 minutes on him I have no idea if I could have done more (i.e. was it good play, or a lucky 'press Q' moment?). I also need to learn Winston, as he's a very good counter to some compositions.