Both my kids have noise sensitivities, my DD was extremely sensitive. For us, I think just being aware that the difficulty is real, and validating her feelings helped the most. It is easy to be dismissive and presume that the kid is overreacting, and at times I needed to remind myself that her anxieties, fears, whatever you want to call them, related to noise were very real. Times I remember with mild regret are things we were usually persuaded to do against my better instincts- fireworks, even though they were distant, an IMAX movie with grandma, even though I suspected it would not go well (they had to leave shortly after it began, etc). We didn't avoid noise altogether, but we did search out and find calm, quiet environments- this was particularly important for preschool. Even the toilet flushing and the bathroom fan in this tiny, quiet school were difficult for her to get used to. But the important thing is, she did. She went to a largish public school for first grade, and though it wasn't perfect, she handled the environment fine.
We also used noise-canceling headphones when she was small. My family plays in concerts frequently (classical, often In churches or small auditoriums, so these are not what I would consider loud) and she could tolerate it only with the headphones on (again, this is a non-issue for her now, she plays in her own concerts). We vacuumed infrequently, when she was not around, avoided the blender, avoided movie theaters, I could go on but you get the picture. And we were pretty aware of her needs in large groups, at parties or other gatherings, just making sure she had an out if she needed it.
I would say her most difficult years were up until age 5 or 6, and now at 14 you would never know she had issues with noise in the past, except that I think she has exceptional hearing😉.
Regarding the anxiety, we did gradual desensitization-type stuff (not formally, just trying to get her used to a more normal sound diet). At a later age we tried a therapist, but couldn't find one with which she felt comfortable; again, this is an issue that mostly resolved itself as she matured and developed coping mechanisms.
