1- Can you please suggest some other alternatives that I could use to suppress my desire for music when I might be working, exercising, etc?
2- What should I do if I have a doubt about whether the music is haram or halal?

1- Take a nature walk. It gives you relaxation

2- Listen to nasheeds that don’t have haram music.

3- Choose music that’s soothing but is not considered “entertainment” music.

4- Train yourself to mention God’s name when exercising. After a while you will feel the amazing impact it has on your soul. For instance, keep saying La ilaha illa Allah when exercising. Or here someone recite it like this one:

https://youtu.be/psN1gCbTgLc

If you have a doubt, as long as you don’t think it’s entertainment music, then you can listen to it