Paula Abdul was so shaken by the apparent suicide of an obsessed fan outside her Los Angeles home three weeks ago that she hasn’t slept there since.

“I’ve been staying in different homes and hotels, and I have security with me,” she tells PEOPLE.

“It was very tragic and very upsetting to hear,” Abdul says of the death of Paula Goodspeed, a fan who auditioned for American Idol’s fifth season. “She had tried to do this before, and it was just heartbreaking … It was in the middle of Hollywood week, and it happened while I was actually working at the Kodak Theatre, and it was devastating to hear.”

While producers were informed shortly after police discovered Goodspeed’s body, no one let Abdul know until after they had finished taping Idol for the day. “It wasn’t fun,” Abdul says.

The tragedy came in the middle of an extremely busy time for Abdul, who, besides working on the new Idol season, recently taped a new MTV cheerleading squad competition special, Rah!, (which airs in January) and has been preparing to launch her Forever Your Girl accessories line on HSN Monday night.

Yet work, she says, “gives me diversion. I always feel like if I can divert my brain to something else then I’ll be okay. That’s why I like to multitask.”

She is also thankful to others for their help during the ordeal. “I have my family, and I have my good friends who’ve completely opened their hearts and their doors to me, which is great.”

Abdul says she is now preparing to put her house on the market: “I am in the process of looking for another place to reside.”

Reagrding details of Goodspeed’s obsession, Abdul has been told not to talk about it, given the ongoing police investigation. “I’d love to tell you so much more,” she says, “but I’m holding my tongue.”

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