I can sightread almost all maps from 4-4.5* (including some old mapping styles/modern cancer) and everything from 4.5-5* is based on the mapping style. If it is a standard TV size I don't even realize it's over cuz short and easy, same for longer maps with standard mapping styles.
I only get nervous on 5min+ maps, no matter if it's easy or hard. FCing 5minute maps is just so satisfying, depending on the difficulty my nerves go from "doped with caffein to cocaine". Never had the feelings you described, though. I reverse choke often due to my "no retry" policy so I couldn't care less about another "good" A rank. If I can't do it again, it was luck and if I do it again I was
consistent.
There was that one time where I actually felt miserable after finishing a map and now my mind blocks on that map. After FCing the first half I feel like passing out, it doesn't happen on other maps, just that one specific map that is not even hard :@ It's this one:
https://osu.ppy.sh/b/53554?m=0 I literally missed the last note on a 7 minute map, the first time I ever said "fuck that" loud, closed my pc, lighted my cig and took a break from a game cuz rage. No game made me that mad and your description fits to that map, but only that one.
Oh and by the way, the only way to stop caring about FCing is to FC easier stuff until harder stuff doesn't feel hard anymore. I always start my osu! sessions with 4* maps and casually FC them when I'm slowly warming up. When I feel ready and my aim is on point I start playing 4.7-5.24* maps and guess what, I don't even care anymore if I'm setting a new top play, because I FCd so many maps already so I start giving a fuck. One exception, 5min+ maps.
TL;DR: Play more and play
diffrent stuff. Just play to improve and if you become better you can go back to your cursed map and sightread it.