I always thought the name of the movie was “Billy” but i’ve searched repeatedly and have not such movie.
What I remember: there was a woman, a singer named Billy (or maybe I remember it wrong). I guess she moved from one city to another and tried ro pursue her singing career. There was a guy who helped her and they started dating if I remember correctly. I remember a scene where Billy and the guy were driving (rather stopped at traffic jam) and they heard her song from the radio for the first time. The guy got out of the car and put everyone elses radio on the same channel.
I believe I saw the movie between 2004-2008 so it’s rather old.