Elizabeth Vargas said she spent the weekend answering her sons' questions about her battle with alcoholism

By Char Adams
Updated September 12, 2016 02:20 PM

Elizabeth Vargas is relieved after opening up about her battle with alcoholism and anxiety in a special edition of ABC News’ 20/20.

“I’m incredibly overwhelmed and grateful for the reaction that we got,” Vargas, 54, said during an appearance on Monday’s Good Morning America. “I’m still getting it as I speak – it hasn’t stopped since Friday night – from people out there who are suffering from similar issues.”

Vargas told Diane Sawyer of the crippling anxiety she experienced during her years as an evening news anchor: “There are days when you wake up and you feel so horrible that the only thing that will make you feel better is more alcohol. That’s when you’re in the death spin.”

For more on Elizabeth Vargas and an excerpt from her memoir, pick up the latest issue of PEOPLE, on newsstands now

Vargas told George Stephanopoulos on Monday that, before the special aired, she told her two sons – Zachary, 13, and 10-year-old Sam – all about her journey because “I would never put them in the position of learning something for the first time on national television.”

However, she said the children hadn’t seen footage of their mother hung over at a shoot.

“Zachary turned to me and said, ‘Wow, mom. You looked really bad,’ ” Vargas revealed with a laugh.

She said she spent the weekend answering her sons’ many questions about her struggle.

“They did not know, George, that you can die from alcohol, and that was the biggest thing they kept asking, ‘Well, how do you die? What do you mean you can die? What happens to your body?’ ” she said. “And I explained all that to them.”