Can my child be exempt from music lessons?

Poor thing. This seems unacceptable. I recall doing theatre in high school (in tech as well before lighting was LED) and specifically thinking I never wanted to work in sound. Long story short: I now work in sound.

Before I go further, I'd suggest to book a hearing test with your GP, so you have physical proof of how acute her hearing is. This is something sound technicians do for insurance and legal reasons. 

I discovered that most schools won't have properly treated and acoustically-tuned rooms, and often badly designed speakers, systems, harsh frequencies bouncing in painful ways due to construction materials even. This combination can properly damage hearing at a young age. Especially, as Autistics and ADHD kids do not dull our senses like our peers. 

While learning to play music on an acoustic instrument is incredibly good for intellect and can be far more soothing in the right environment, sound is weaponised, and been used in warfare and - though this won't be happening at school - is well known to kill humans at particularly low frequencies. Sometimes, you can reason with what would be kind to a dog, since this child's hearing is closer to that of a collie. 

Immanuel Kant wrote in one of his critiques on Sensory experience and aesthetic, ranking sound as the lowest aesthetic simply on the basis that one cannot just escape it if need be. Sound carries and penetrates through forests and walls. It is invasive. Not everyone pauses to think of the "darker side" of music.

Short of hiring an independent music teacher to take her elsewhere to learn an instrument during these classes, it may be worth-while to exhaust the internet looking for ear defenders or plugs she will wear.  If she can learn to put cheap foamy ones in even, they can be helpful. Another idea is to speak with the music instructor. If they understand a little bit about acoustics, perhaps there's a spot in the room which is easier to sit and observe from. This would be a matter of walking around the room and finding a safe spot to sit.

Even though I have amazing hearing, I also have tinnitus; permanent ringing for life. 

As for frustration, can she go for a run? jumprope? Or something else to redirect the built up frustration? It's not immediate but it's good to start learning that we are impacted intensely due to less internal filtering as signals to our sense perception are always incoming. Far more intensely than those who are not Autistic or ADHD. As I got older I've learned a low dose of anti-anxiety medication in a pinch (never daily) is a valuable resource and appears to match the medical reports for its specific use (lower GABA). 

Poor thing. This seems unacceptable. I recall doing theatre in high school (in tech as well before lighting was LED) and specifically thinking I never wanted to work in sound. Long story short: I now work in sound.

Before I go further, I'd suggest to book a hearing test with your GP, so you have physical proof of how acute her hearing is. This is something sound technicians do for insurance and legal reasons. 

I discovered that most schools won't have properly treated and acoustically-tuned rooms, and often badly designed speakers, systems, harsh frequencies bouncing in painful ways due to construction materials even. This combination can properly damage hearing at a young age. Especially, as Autistics and ADHD kids do not dull our senses like our peers. 

While learning to play music on an acoustic instrument is incredibly good for intellect and can be far more soothing in the right environment, sound is weaponised, and been used in warfare and - though this won't be happening at school - is well known to kill humans at particularly low frequencies. Sometimes, you can reason with what would be kind to a dog, since this child's hearing is closer to that of a collie. 

Immanuel Kant wrote in one of his critiques on Sensory experience and aesthetic, ranking sound as the lowest aesthetic simply on the basis that one cannot just escape it if need be. Sound carries and penetrates through forests and walls. It is invasive. Not everyone pauses to think of the "darker side" of music.

Short of hiring an independent music teacher to take her elsewhere to learn an instrument during these classes, it may be worth-while to exhaust the internet looking for ear defenders or plugs she will wear.  If she can learn to put cheap foamy ones in even, they can be helpful. Another idea is to speak with the music instructor. If they understand a little bit about acoustics, perhaps there's a spot in the room which is easier to sit and observe from. This would be a matter of walking around the room and finding a safe spot to sit.

Even though I have amazing hearing, I also have tinnitus; permanent ringing for life. 

As for frustration, can she go for a run? jumprope? Or something else to redirect the built up frustration? It's not immediate but it's good to start learning that we are impacted intensely due to less internal filtering as signals to our sense perception are always incoming. Far more intensely than those who are not Autistic or ADHD. As I got older I've learned a low dose of anti-anxiety medication in a pinch (never daily) is a valuable resource and appears to match the medical reports for its specific use (lower GABA).