You have two serious problems. You don’t have friends and your family is falling apart. No wonder you are feeling stressed and unhappy.
You are not at all alone in having difficulty with lots of moves that meant repeatedly leaving your school and adjusting to a new place. Military kids often have the same problem. So do kids whose parents’ jobs move them around a lot. Kids often end up feeling out of control of their lives and like there’s no use in even trying to make new friends when they are only going to have to leave.
Managing multiple moves means thinking about it in a different way. The key is joining something that interests you at school or outside of school. Join the same kind of club or team at each move and get to know the kids who share that activity. Stay in touch with kids you’ve left behind through the Internet. Pretty soon, instead of no friends, you will have friends who share the same interest wherever you go. Because they share the same interest, the kids in each place are interested to know about how things were done in your former place.
I know one kid, for example, who is a figure skater. She finds an instant group of like-minded kids wherever she goes as soon as she hits the rink. Another kid I know was a Girl Scout in the U.S. She has connected with Girl Guides in many countries and keeps in touch with the various groups on Facebook. She’s a little older than you (19) so has been able to go back and visit other girls in 3 countries during summer holidays. Your job is to stop spending your time feeling sorry for yourself and start taking charge of your life by figuring out what activity you like enough to use as your connector to other people. Yes, I know it’s hard. I know you probably don’t feel like it since you’re so sad. But the only person who can change this part of your life is you.
As for the family situation: Please listen to me: The family problems are not, not, not your fault. Your mother has been diagnosed with a mental illness and your dad has probably been occupied with his career. They are the grownups. It is their job to get whatever help they need to fix the family. At 13, you can’t take your parents’ troubles on your shoulders. All you can do is tell them how sad the situation makes you and that you wish they would find help since you and your little brother need them. if there is a counselor at your school or a teacher you trust, you could ask him or her to help you make that request of your parents and perhaps provide information about where to get treatment for your mom and support for your family.
Please stop blaming yourself and start doing what you can to make your life better. I can tell by your letter that you are a sensitive, caring person. Other people will be glad to be your friend once you let them get to know you.
I wish you well.