The fear, she said Tuesday at Saks Fifth Avenue's 14th Annual "Unforgettable Evening" gala – where the Oscar winner was honored for her efforts to battle cancer through her late father Bruce Paltrow's fund – "sort of swept over me to the degree that I lost my sight for a second and I nearly collapsed."
But then, "I thought of my children and what it would mean to my family," she said. "I thought about the things that I still need to accomplish, and I felt the bitter clinch of this fear wrap itself around every organ in my body until the doctor walked in and told me I was fine."
On the subject of mortality, Paltrow, 36, told PEOPLE that she and husband Chris Martin haven't really planned on what sort of legacy they hope to leave for their two children, Apple, 4, and Moses, 2.
"I just sort of do the best that I can on a daily basis and I learn," she said.
Kicking AssIn the meantime, the actress is keeping active – launching a cookbook and helping her trainer, Tracy Anderson, open a gym, Paltrow confirmed to PEOPLE at another Manhattan event – Wednesday's Cinema Society and Ferragamo-sponsored premiere of her new movie with Joaquin Phoenix, Two Lovers.
"She's opening a gym in Tribeca and I'm helping her," Paltrow said of celebrity trainer Anderson, who puts Madonna through her paces – just as Anderson does Paltrow.
"Yes, she kills me," Paltrow told PEOPLE. "She kicks my ass."
As for that big romantic holiday this weekend, the actress said, "My husband will be on tour in Australia. So, I'll be with my kids for Valentine's Day."