I can’t make a diagnosis on the basis of a letter. But I can tell you that you are right to be concerned. So am I. Since you didn’t give me any information about your background and history, I can’t even venture a guess.
I’m very sorry your parents won’t take you for at least an evaluation by a counselor. If you haven’t told them everything you told me, it might be helpful if you showed them your letter. Yes, you may simply have a very, very vivid imagination. You may have created “friends” since you don’t have any. But it’s also possible that there is something else going on. A one time visit to a qualified counselor would let your parents know which is which. I hope you will consider sharing your letter to us with your parents. Maybe the details you gave us will help them reconsider their position on seeing a counselor.
If not (and since you are home-schooled), you need to look for other adults to help you talk to your folks. Is there a grandparent or other member of the extended family you trust enough to talk to? Your pediatrician is another option. If your family attends a church, the pastor might be helpful.
While you sort this out, I encourage you to use the hotline at Boys Town. Don’t be put off by the name. Girls use the service too. Here’s the website: http://www.boystown.org/hotline/Pages/default.aspx Counselors there are available 24/7 to talk to teens like you. You can chat online or in person. It is free and confidential.
I wish you well.