Trully question. I cannot be the only one who cries when listens music. I was the privellege to see my favourite artists live, but since last year, all lives I assisted on YouTube by Fred again… , I cry . Has been my favourite musician since last year. Almost all songs, for me, are amazing and give me a bunch of emotions.
The tear-jerker songs? Brandi Carlile has a few, The Joke, and the opening track on the Highwomen album (that album has a few). And every single time, the Julie Miller track Rachel makes me cry, also Red Dirt Girl by Emmylou Harris.
Feeling music deeply in general though? No you are not alone. It varies among people, most of us do some of the time, some of us do most of the time.