Jennifer Grey is opening up about how the results of the two nose job procedures she underwent

after the success of "Dirty Dancing" left her feeling "completely invisible" in Hollywood.

The 62-year-old actor, who famously starred as Baby opposite Patrick Swayze in the 1987 romantic drama,

 told People that she bumped into fellow actor Michael Douglas at a premiere

after undergoing the rhinoplasties and he didn't recognize her.

"That was the first time I had gone out in public. And it became the thing,

the idea of being completely invisible, from one day to the next," she recalled.

Grey said her sudden invisibility felt even more "weird" because, unlike her famous parents,

Oscar winner Joel Grey and former singer-actor Jo Wilder, she never wanted to get a nose job.

“In the world’s eyes, I was no longer me and the weird thing was that thing that I resisted my whole life,

Jennifer Grey recalls feeling invisible