Nah, it would be difficult for a hunchback to make all this way to the Aretuzae by herself. And she was younger than 13 when she passed her entrance exams, but Nimue was 16-17, plus healthy. I believe her parents brought her in Aretuzae themselves, because Yen was showing signs of magic and it was a better place, than orphanage. She was depressed and suicidal, because she thought, that no one loves her, she is ugly, deformed, abandoned. I believe Tissaia saw the strength of her will, she even told that her cuts was real, deep, she wanted to die, that was not tantrum from a teenager who was too scared to really die, but her intentions was real. She was really strong and brave girl, to be not scared of death in her 11-12 years.