Remember, God loves your little sister even more than you do. Jesus said that "the angels of children are always before my father." Each day before you rise, say a prayer for your sister. Commit her to God's care. Say something like this, "God, I know you love my sister even more than I do. And I thank you for watching over her today. I ask that your angels will and protect her from all harm today. Thank you for keeping her safe in your care all day. Amen," Then trust in God to answer your prayer. Let it go. Don't think about it anymore. She's in God's hands now. You have committed her to God and she's safe in His care. You can trust God to take care of her.
Your fears are irrational...I had the same type of fears as a child (teen) also. I was always afraid of something happening to the point of craziness! I always feared my parents were going to get in a car accident, or if my sister was late coming home that something bad happened. I still have a lot of these anxieties at 42! I suggest that you speak to your parents about how your worries are out of control and are affecting your life. Maybe you should get some counseling. I wish I did when I was younger because now I suffer badly with anxieties. If I took care of it when I was younger I bet it would have been easier now for me to deal with.
It is natural to care for someone so young. You are a good person for doing that. But you are making it an obsession. So much so that it is making you sick with worry. Can you not rationalise the situations? Home = Safety. Even when she is out she is with an adult or been looked after in school. Get those thoughts into your head. Because the day is going to come when she gets older. Then what? That first date and the likes. She will want her independance and might see you are overdoing it and it could all begin to backfire on you. And that is something we don't want to see happen. You sound like a good, kind, caring person. Someone who only wants to do the right thing. The right thing for now is not to worry so much. Accept that she is in safe hands when out and that your house is a safe place too.