After spending a few years in Zambia, the pair decided to make yet one more move, this time heading to a camp in Malawi that had better living conditions and even better schools. They arrived in September 2000.
Twayigira immediately enrolled in school once she arrived, making several new friends and, for the first time since they had left, was happy to have adequate food and shelter.
Being able to do well in her classes "would give me joy. Because at least I got to make some people proud, and I was very happy," she said. Twayigira was eventually selected to join a Jesuit-run school, with all fees paid for by the Jesuit Refugee Service.
When she finished school in 2007, Twayigira's grandfather fell ill, passing away just a few days after.
"I cried uncontrollably, badly, but life had to go on, and although I was in so much pain with the loss of my loved ones, it did not stop me from working hard," she said, "because I knew that my future, it was not certain, I did not know what my future had, but I knew that my hard work would pay off."
In 2009 she studied for the national final exam in Malawi, and finished among the top 6 students in the country. At the awards ceremony, the Chinese embassy offered a number of full-ride scholarships to study in China for the top students.
Twayigira was one of the students selected and, despite being a refugee with no citizenship status or passport, was able to get her paperwork in order with the help of the Jesuits at her school, a Catholic radio station and even the Malawian parliament.
She then moved to China and studied the language for a year before officially beginning classes in Chinese. She has since graduated and is currently working as a medical intern in Malawi.
While there were many times she wanted to give up along the way, Twayigira said she persisted, because at a certain point she realized that "God spared my life" not to keep it for herself, but because "there are people that I was meant to serve."
"Before I went to China, I used to think I was just this girl with a tragic past...but when I got to China I realized that I've got a story to tell; a story of God and his love, a story that can change somebody's life."
As a doctor, Twayigira said she feels she can give even more. But in addition to her medical duties, she also looks for opportunities to speak in schools to try and "raise hope among the youth, especially refugee youth."
She said that in the future, she hopes to work more directly with refugees, "because I believe I have a lot to share, having gone through what they've gone through."
"Now this is my story...but unfortunately for many, theirs is just in the tragedy part," she said, explaining that many refugee children don't even have access to adequate housing let alone higher education.
Even those who do get a good education don't necessarily have the same opportunities, Twayigira said, so "their hopes are just crushed."
In order to change the situation, she said war itself has to end: "why not end all this violence, and I'm not talking about people from other countries coming in to invade our own countries, I mean why wait for an outsider to come to stop hurting, and killing?"
"Is the money or power at the expense of their blood really worth it? I don't think so," she said, adding that the only way to really resolve conflict is with "forgiveness, mercy and love."
"Is there such humanity in us, or have we become robots?" she asked. "What is happening to innocent kids is completely unfair, and it needs to stop and I believe it starts from within us: from love, forgiveness and mercy."
People in situations similar to hers need to know "that they are loved by God and people around them. They need to know that they matter, that there is hope for them, that they have a purpose in life," she said, noting that this stems not only from having the basic needs met, but above all from education.
In an interview with CNA after her talk, Twayigira stressed the importance of education, saying it's "really the key to everything, because if not educated, many girls don't even know their value."
However, with a good education women learn that "okay, I'm not worthless and someone can't just come and step on my foot. I am somebody," she said, adding that a proper education helps women to step into decision making positions where they can change things.
"I believe that once a girl is educated, that means you're actually educating the whole family. Because a woman, you raise your children, they're with you all the time, you know that whatever they get is what you teach them," she said.
"So if a woman is educated that means the whole family will get quality advice from their mothers. So educating a girl is actually educating the whole country."
Twayigira said she was happy to be able to speak at the Vatican, since the event was streamed live. She voiced her hope that people can hear her story "and not just feel sorry for me, but also see ways they can help other people like me to get a better education or a safe place, or open their homes to refugees like me."
She said she also hopes other young women and girls from around the world will be able to see and hear her story, and to know that "it's all possible...I believe that I'm a pillar of hope for them."
She said one of her hopes coming out of the conference is not only to encourage young women in her situation to have hope, but also that the people who have the power and resources to change things will see that they "can actually do something under-privileged people like I was."
"Their actions can change somebody's life for the better, never to be the same," she said.