"I was in this position where I was going through puberty, and I developed very quickly," the actress recalls of growing up in the spotlight

Soleil Moon Frye was just 7 years old when she became a household name, thanks to her role as the titular character in the hit children's series Punky Brewster.

"Punky is still such a huge part of my heart and soul," says Frye, now 44, who shares her memories and intimate home videos and diaries in her new documentary, Kid90, launching Friday on Hulu. "If I'm 88 and people still want to call me Punky, I'd be thrilled."

But when the series ended in 1988, a preteen Frye was adrift — and found herself attracting the wrong kind of attention.

"I was in this position where I was going through puberty, and I developed very quickly," she tells PEOPLE in this week's issue. "Everywhere I went I was called Punky Boobster, and people would stare directly at my boobs."

soleil moon frye
Soleil Moon Frye
| Credit: Diana Koenigsberg
soleil moon frye
Credit: Diana Koenigsberg

For more from Soleil Moon Frye, pick up the latest issue of PEOPLE, on newsstands Friday, or subscribe here.

The actress recalls being offered "tits and ass roles" and the discomfort she felt in her own skin.

"No one is in charge of how their body develops," says Frye. "But there was so much shame about it."

Soleil Moon Frye - kid 90
Credit: Courtesy of Soleil Moon Frye

Eventually, Frye decided at age 16 to have breast reduction surgery. "My shoulders had indentations, I had back problems, there were so many different issues," she says.

She decided to go public with the surgery to promote a healthy self-image, but says that with the resulting headlines, "the message was lost."

soleil moon frye
Credit: The Life Picture Collection/Getty

Eventually, Frye, who is now a mother to four children with her ex Jason Goldberg, learned to love and accept her body — and her true self.

"My experiences made me who I am today," she says. "And as much of a roller coaster as it was, I wouldn't change one thing."

Kid 90 launches Friday on Hulu.