I work in a mail processing plant and the music is too distracting and loud. Every night it feels like I'm walking into a dance hall. I informed my supervisors and Health and Safety representatives took their cell phones around to each speaker/radio and came back and said the noise level was 30 decibels below the unacceptable level. They told me to wear ear plugs. Every night I dread going to work because of this and I've had migraines on 2 occasions. I've complained on several occasions and nothing is being done. What do I do next?
If ear plugs are unacceptable to you, you could invest in a good set of noise cancelling headphones.
You don't need to listen to music through them. If you play some white noise then a decent pair can drown out a surprising amount of background noise.
The next step is to wear the earplugs.
A lot of people have to deal with distractions and noise. If it wasn't music, it may be mail processing machines. Would you demand the machines be turned off while you work?
The simple fact of the matter is, your employer is trying to improve the enjoyment of the environment for people. There is an easy thing you can do to make sure everyone is happy. I don't see any justification on why you don't think this solution is suitable.