The 36-year-old said she convinced herself the worst would happen after hearing nightmare stories, and was unable to let go of her baby, whose father is her ex-partner Liam Payne, reports thesun.co.uk.
"When I had him, first of all I wouldn't let the doctors take him out of the room. I read this story about two girls being swapped at birth and it was playing on my mind," she said during a podcast.
"I was so irrational. I didn't want anyone to take him."
Cheryl and Liam welcomed their son in March 2017. The couple later parted ways.
Liam, 26, recently admitted that Cheryl remains "one of the most important people" in his life.
He said: "Becoming a dad at such a young age, it's such a difficult thing. And I think I built fatherhood up so much in my head that it kind of messed me up to start with. I started in a bad place with it.
"I think it spooked me out early on, and I was just worried I would not be enough to look after the both of them. They're so important to me - Cheryl as well.
"She's one of the most, if not the most, important people in my life. I'm lucky I have someone who understands what I'm going through," he added.
( With inputs from IANS )