This is way too big a problem for a 13-year-old to handle on her own. Please think hard about what adult in your life might be able to help your parents understand that you and your family need help. You don’t know how to manage your anger. Your folks don’t know how to manage you. Everyone is getting frustrated and discouraged – so much so you are all ready to give up on each other.
You’re clearly a sensitive and caring person. You’re right that what’s needed here is some therapy. I suggest you think about talking to your school guidance counselor, your religious advisor, a trusted teacher, or the parent of a good friend. You will know who your parents just might listen to. Ask that person to help you tell your parents the things you talked about in your letter. When you do talk with your parents, work extra hard not to get angry but rather to express your sadness and pain. Also have on hand some phone numbers for a local mental health clinic.
If your parents refuse to get involved with therapy themselves, ask again for help finding someone to talk to. Tell your parents that you aren’t interested in blaming and being angry but that you want to learn how to handle your anger and express your feelings appropriately. Sometimes when one person in a family starts therapy and starts showing some results, other people in the family get interested in doing it too.
Meanwhile, live as healthy a life as you can. Get involved with activities where you will meet people who are likely to become good friends. Eat right. Make sure you stay active. Believe it or not, dressing well will also help you feel better about yourself each day. Do these things as a statement that you value yourself – even if some other people don’t. That atttitude will help you attract the kind of friends who can be there for each other.
I wish you well.