"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.
Ill-Timed TragedyThe 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 Dec. 13 and 14.
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."
Obsessed FansAbdul similarly could not comment on the flowers Goodspeed had sent to her just before the apparent suicide, or how many times she had encountered Goodspeed since her infamous Idol audition.
This is not the first time Abdul has dealt with an obsessed fan. In 1993, "this gentleman was writing letters everyday from prison saying he was getting out in 120 days, then 119 days, all the way down to he's getting out and he's coming to get my mom and I," she recalls.
"Thank God we were in Canada for my touring, and after that we were in Washington and he made a threat against the President, so he's in jail for the rest of his life," she says. "He had tattoos of me all over his body."
After getting through her accessories launch and the new season of American Idol, Abdul says, "I'm going to go on a vacation of some sort. I haven't taken a vacation in a long time. And I'm gonna go far away so no one can find me!"
2005: Paula finally ends her battle with chronic pain