I should preface this by saying this is not related to the Civil War. After searching around, I've seen similar issues stem from parts of that, but I haven't started anything Civil War related with this character.

Basically, every single time I load up one of my characters, it never stops playing combat music, even though I'm not fighting anything hostile. I've tried several of the console commands to attempt to fix it, like "StopCombat" and "SCAOnActor" but they haven't helped. I spawned a dragon and killed it, which temporarily stopped it, but then no other music would play, not town, explore, or anything, it was silent. Then I'd reload it again and the battle music is back, non-stop. Starting to drive me up the wall.

Weirdly, it's only on one character where this is a problem. I loaded up a newer character and everything works perfectly fine. Any help would be greatly appreciated!

Oblivion had the same issue for me before, but I don't think I encountered it in Skyrim. Did you try just standing in one spot for a few minuets to see if it goes away?

Disable all music and enjoy the beautiful background sounds of Skyrim

Yeah, I stood and ran around for a while and it looped through three or four different battle tracks without ending. Like I said, I can get to stop for a bit by killing a dragon, but it happens every single time I load up that particular character, regardless of where I am or what I'm doing.