"I felt like I was in a black hole and I couldn't see out," Joel, 24, reveals in the new issue of PEOPLE. "I hit rock bottom that day . . . A part of me wanted people close to me to know – not the whole world."
The trigger for her depression? A very bad case of heartbreak. Joel says she never really got over her first love, her former bassist Jimmy Riot, whom she began dating at 19. They broke up in 2008, but had fleeting reconciliations. "I was addicted to this man," she says, "and it spiraled out of control."
Joel now sees a therapist regularly and is talking more openly to her parents. But tabloid reports that her overdose stemmed from a fight with Brinkley over her weight still upset her.
"It had everything to do with my depression, my anxiety, a dysfunctional on-and-off relationship with my ex – nothing to do with my relationship with either one of my parents," she says.
In fact, Joel says, "Nobody is more supportive of my physical appearance than [my mother]." The singer adds, "She tells me – which I don't understand – that she wishes she looked like me, that I'm so much more unique than her."
Joel is now following in her mother's modeling footsteps, appearing in commercials for Prell shampoo – 25 years after Brinkley's gig as the company's spokesmodel.
While the singer, whose new album is due in June, understands her ad will be compared to her mother's, she is committed to creating her own identity.
"It's hard because [people] compare my music to my father and my looks to my mother," she says. "And I like to think that my music and my voice are different than my father's and my look is very different than my mother's. Can't I just be me?"
For more on Joel's heartbreak and her fresh start pick up the new issue of PEOPLE, on stands now