The 51-year-old also revealed that her two youngest children, Bella and Anwar Hadid, were also diagnosed with Lyme disease in 2012.
"[God] changed my destiny," Foster said. "Watching my babies struggle in silence in order to support me in my journey struck the deepest chord of hopelessness inside of me. ... I will walk to the end of the earth to find a cure so that you can live a healthy life that you deserve. No child should suffer the way that you do."
ET spoke with Dr. Daniel Cameron, President of the International Lyme and Associated Diseases Society, at the event about the likelihood of multiple family members being affected by Lyme.
"It's actually very common, because they share the same lifestyle," he said. "Many people find that when one person is identified and starts getting to know the symptoms of Lyme, then they realized someone else in the family is also ill."
Dr. Cameron also praised Foster's decision to speak out publicly about her health struggles.
"It's helped a lot of families look a second time at their child and realize their child doesn't have normal, routine childhood problems," he said.
Prior to her emotional speech, Foster was introduced with a touching, tearful tribute from her daughter, Gigi Hadid.
"I remember when she was going into the first season of filming [Real Housewives], she said to me ,'I don't know why this show was brought to my life but, for some reason, I think it will lead to something bigger,'" Hadid recalled. "My mom is usually right, but this time she was really, really right. She had a purpose. She realized that she could use this platform of this world famous television show to spread awareness."
Hadid continued, "She was honest, unapologetic and raw in how she portrayed Lyme disease on social media and on the show from the second she announced to the world that she had been diagnosed."
The 20-year-old model also choked up on the red carpet, speaking with ET about how -- as Foster's only child without Lyme disease -- she is staying strong for her family. See the interview in the video above.
Foster's husband, legendary music producer David Foster, also praised his wife's courageous battle in an interview with ET, while her RHOBH co-star, Kyle Richards, fought back tears. Watch below.