"I went in thinking there was something else, maybe a really upset stomach," Jeanne Hecker, 34, tells PEOPLE. "But they did an ultrasound and they're like 'No, you're pregnant.' "
"This is a joke, right?" Hecker, a cashier from Covington, Louisiana, asked the hospital staff.
But it was no joke; Hecker delivered a healthy baby girl.
Kylah Grace was born at 7:57 p.m. on Saturday. She weighed 6 lbs., 3 oz., and measured 18.5 inches.
"It's still pretty surreal," said Melissa Hecker, Jeanne's sister.
Jeanne, who thought she couldn't have children because of a medical condition, agreed.
"I had given up on the fantasy of having a baby," Hecker said. "It's crazy, now I have a whole human to take care of. She's mine. I made her."
Jeanne, Melissa, their mom, Emma, and other family members had to quickly come up with a name for their newest member.
Their mother suggested "Kylie," but "Jeanne said she wanted something that sounded prettier, more unique," explained Melissa.
So their mom suggested "Kylah," which Jeanne liked, Melissa says.
The baby's middle name – Grace – was inspired by her eyes and, of all things, the weather.
"Her eyes are graying blue and it was also raining and we were debating 'Rain' or 'Storm,' but settled on 'Grace,' " says Melissa.
"It was the best feeling," says Hecker of holding her baby for the very first time. "Now I'm just trying to look at her and get to know her."