Breath control and confidence works.
What helps with the confidence, I find, is finding a ‘secure’ practice room, i.e. a room where you aren’t constantly worried about who might have heard you or what they might say. You need psychological (not to mention acoustic) space to try things out.
For extra practice and to overcome fears of the upper register someone taught me to start my practice sessions with two warm-up scales (here on treble/alt). The first is the C major scale starting on the D above the upper C and going down, the second is the F major scale starting on the high g. This way you are starting your practice sessions with two of the most difficult notes (aside from the high F sharp, etc.). It’s very satisfying when you can begin to hit these two notes just right (at least some of the time) ‘cold’.