I was terrified myself when I moved here to New Haven, CT back in 2003 for my PhD. My parents were terrified as well. But you know what it will pay off big time. I have grown so much since been here at Yale for the past 5+ years. You wont be alone in this. There are so many students here at Yale who will be here on their own for the first time and they will be as scared as you but you will be fine. You will meet new people who will become like your surrogate family.