I understand how frustrating it is to feel that you do not fit in.

Do you start conversations with classmates during classes? Have you considered taking part in the activities that do not require pre-regsistration with a group, or, just randomly asking classmates whether they would like to join with you? Give it a try! I think you're just lacking a tiny bit of confidence in yourself. What's the worst case scenario? Some may turn you down. But some may be happy that you approached them! You said you find people at the boarding school nice. Use this at motivation to get you started. And if it so happens that you get some rejections, don't get discouraged! Be proud of yourself at how far you've come and continue starting conversations with others! Someone worthy to be your friend will surely notice, sooner or later. I wish you good luck!