Depending on where you live it and the job you do, you may be possible to get an exception to the rule against wearing headphones.
If you’re in the US or UK, I know it would be your right to request reasonable accommodation for ADHD - either under the ADA or the Equality Act.
Obviously if there’s a good reason to disallow headphones (for example, if there’s some danger that you wouldn’t be able to hear) then this wouldn’t help. But if it’s just the company being controlling, you can probably get an exception.