August 17, 2016 01:45 PM

Jax had reached her limit.

“I was living out of a suitcase and spending all my time in the recording studio or performing,” the singer, 20, says of the months that followed her third-place finish on season 14 of American Idol in 2015. “And emotionally, I was all over the place.”

Feeling depressed and homesick, Jax – who was born Jaclyn Miskanic – returned home earlier this year to spend time with her parents and brother in Atlantic City.

“We were at the grocery store when I first felt something wrong in my throat,” says Jax, who is featured in the current issue of PEOPLE. “But I’m always getting sick, so we thought it was a sinus infection.”

The doctor she visited assumed the same, but had her take x-rays as a precaution.

“I didn’t think anything of it,” Jax says of being cautious.

But the x-ray revealed 18 tumors – 12 of which were determined to be cancerous.

“I had some important things going on so my parents waited a day to tell me after they found out,” Jax says of her thyroid cancer diagnosis. “They sat me down and told me, ‘We need to talk.’ I actually thought, ‘Oh no. What did I do now?’ ”

Steven Tyler and Jax performing on the Idol finale in May 2015
Frank Micelotta/FOX

For more on Jax’s health battle, pick up the latest issue of PEOPLE, on newsstands Friday

The U.S. women's gymnastics team on the cover of PEOPLE: (left to right) Laurie Hernandez, Aly Raisman, Simone Biles, Madison Kocian and Gabby Douglas

The doctors wanted to act swiftly, but Jax had a big fear going into surgery: “I was worried I’d lose my voice forever,” says Jax, whose grandfather also had thyroid cancer and has not been able to speak since his surgery a few years ago.

Jax went under the knife this spring and had her entire thyroid removed, along with the cancerous tumors and several lymph nodes.

She’ll undergo chemotherapy through the end of the year, and it’s still painful for her to sing, but Jax is already working on her return to the stage and plans to run the New York City Marathon in November.

“It’s therapeutic for me to run,” says Jax, who is using the marathon to raise money for a 9/11 charity. “I look at crossing that finish line as kicking cancer’s ass.”

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