The scholars differ on this. Some are in the opinion that singing is alright, music is not.
While the strictest opinion is singing is alright only
I feel I have ADHD, I wasnt diagnosed ever, but I also am from a third world country where mental illness isnt a thing people think about. I myself found out something like ADHD existed from online friends and I have found I have a lot of symptoms, now it doesnt really matter whether I have ADHD or not, it doesnt change me being randomly hyper, or having attention problems, or memory problems etc etc.
Anyhow my point is, I do similar things like you as I cant stand absolute silence, my mind is always running as long as I am awake. I used to listen to music growing up and used to always have earphones in my ears. When I became practicing it turned into just listening to some Nasheeds, now after several years I no longer sing but find myself randomly talking loudly as if I am talking to an audience (i became a youtuber so thats where practicing loudly came from).
I am surrounded by lots of sound triggers right now, like a loud keyboard (blue mechanical switch) which never stops bc I am always using the keyboard most of the time in my day anyway.
Also have a few of fidget toys for when I am away from my pc that makes sounds that I can hear when I fidget with them.
Plus ADHD itself is a disorder and as much I dont think general rules apply to people with this mental illness. However for concrete conclusions, its better to consult knowledgeable ones i.e. scholars.
btw whats your experience with concentration