One of the best music teen angst film is Pump Up The Volume. The film was released in 1990, written and directed by Allan Moyle and starring Christian Slater and Samantha Mathis.
If you've never seen it, it is about Mark Hunter, who just moved to Phoenix, Arizona. He's a little anti-social, and expressed himself through a personality called Happy Harry Hard-On via a small FM pirate radio station that broadcasts from the basement of his parents' house. His station is popular with his high school and, of course, the FCC (Federal Communications Commission) eventually stepped in and try to stop the pirate broadcast.
As the movie's theme song, "Everybody Knows" by Leonard Cohen plays over the opening credit, you get a glimpse of Hunter's "underground" bands on cassette tapes: The Jesus and Mary Chain, Camper Van Beethoven, Primal Scream, Soundgarden, Ice-T, Bad Brains, Concrete Blonde, Henry Rollins, and The Pixies (see image below).
Pump Up The Volume's soundtrack still holds up, as does the film. Although, I do find it hard to believe that some of the actors that appeared in Pump Up The Volume are teenagers, despite the fact that Slater previously appeared as a teenager in Heathers.
If you enjoyed Pump Up The Volume, other films, from this era, worth checking out: Say Anything... (1989), Dazed And Confused (1993), Singles (1992), Empire Records (1995), and, of course, Trainspotting (1996).