Piece of Mind by Michelle Adelman

When Lucy's father passes away, she has to go and live with her younger brother, Nate, in New York City.  Lucy had a traumatic brain injury at three years old--she was hit by a truck and cannot live on her own. Nate's and Lucy's relationship is further complicated by the fact that Nate has had to leave his university and get a job because their father died without any savings. While Nate is working, Lucy spends her days getting to know her new neighborhood. Soon, Lucy finds herself making friends and learning that she is a stronger and more competent person then she ever realized.