Meghan Trainor was convinced she didn't have the "face" or body to make it as a pop star.

The 22-year-old, who recently won Best New Artist at the Grammy Awards, became a star when she released her first hit All About That Bass, an anthem encouraging people to embrace their curves.

However, Meghan admits she hasn't always been so self-confident, and she used to make an extra effort to hide her body from the world.

"I, every day, wore sweatshirts and sweatpants to cover up my body, because I was so insecure," Meghan tells CBS correspondent Tracy Smith in a new interview. "And it would be summer. And I would go on vacation and I'd be in Trinidad and Tobago, 90-degree weather, and I'd be wearing sweatshirts that said (her hometown) 'Nantucket'."

Despite family members encouraging her to wear more weather-appropriate items, she refused.

"I didn't want to show my arms," she recalls. "I didn't want to show anything, and I was just so insecure and uncomfortable, and I thought, 'All right, if I'm fully covered - I'm good.' And that's not what I should have been feeling."

Meghan's insecurities made their way into her professional life as well, since she was convinced she wouldn't be able to find success as a pop star as she wasn't typically slim, like most young singers.

"I see pictures of my face and I'm just - I'm like sad, and I'm in a sweatshirt and I'm in my room producing because I just turned off the idea of, like, 'You'll be the face (of pop music).'"

But, following the 2014 release of All About That Bass, she felt empowered again, thanks to the encouraging messages from fans who struggled with the same insecurities she did.

"I get messages all the time: 'I hated myself, I didn't wanna go to school. I was so uncomfortable, and now I love myself. And I was in a really dark place until your song came out,'" she remembers. "And I was like, 'Whoa, man, we gotta do more of these songs!'"