Jack Osbourne and Sharon Osbourne
06/24/2012 at 01:00 PM EDT
It's been a week since Jack Osbourne announced
he had been diagnosed with multiple sclerosis
, news that he told PEOPLE came with anger and frustration.
But Sharon Osbourne says her son, 26, is now feeling "fantastic."
"He really is," she told reporters Saturday on the red carpet at the Daytime Emmy Awards, in which her show, CBS's The Talk
, was a three-time nominee. "He's very, very strong."
She added: "The outpouring for Jack has been amazing. It really picks you up and gets you back into reality when you see how many people care and are concerned. And it makes you feel really strong."
Sharon, 59, also expressed gratitude for the support from the ladies she was walking the red carpet with: her co-hosts on The Talk
(Julie Chen, Sara Gilbert, Sheryl Underwood and Aisha Tyler).
"I think it's just that we're all so caring about each other. You know, we've been working together a long time, and we know a lot about each other," she said. "It's just been an outpouring of general concern for our family from everyone at CBS."
For now, Osbourne, who herself battled cancer
, is enjoying being a grandmother to baby Pearl Clementine
(who calls her "nana"), born in April just two weeks before the diagnosis.
"I love it," she said. "I want more [grandchildren]."
As for her son, he's taking on the role of a parent
"like a duck to water," Osbourne said.
"[It's] as if it was always meant to be," she added. "He's really, really a good dad."