I’m concerned that you are so focused on getting medicine for the OCD that you aren’t looking at the whole picture.
Yes, you may be a “hormonal” teen, but that doesn’t mean that your distress should go ignored. The first stop should be with your regular doctor to make sure your hormone levels are normal and that you are generally healthy. Some of what you are reporting could be caused by endocrine issues.
Do also talk with your doctor about your sleep disorder. It may be more important than you think. You can find information about how to normalize your sleep cycle on the Internet. Do your best to follow recommendations and get yourself back into a regular sleep pattern. I have a guess that doing so will help calm down the OCD at least a little.
Since you have been diagnosed with OCD, I’m assuming that a qualified mental health counselor did the diagnosing. Return to that professional for help in developing a treatment plan and in talking with your parents. Meanwhile, there are a number of excellent self-help books available that can help you learn to manage the obsessional thinking. Go to Amazon or Barnes and Noble and search for a title that appeals to you.
Finally, you are much too isolated. Frequent moves and attending school online means you are not having the experiences that most teens need to emotionally grow. Your mom may be right that you need to “get out of yourself” but that is difficult to do when your only social outlet is with you!
Online relationships can be satisfying but they are not the same as participating in the social environment that school offers. You need a few best girl friends to talk to about your experiences, to normalize at least some of what you are going through, and to share laughs, fun times, music, and hanging out as well as mutual support.
I think you need to go back to school! Yes, you have moved a lot. But, as other kids who are frequent movers will tell you, you can see that as a plus, not just a minus. You have the chance to make friends in lots of places. You have interesting experiences to share with new people. You can develop an ease with doing new things and meeting new people that will serve you well as an adult. It may be scary at first, but put on your big girl pants and get out there! Getting more social experience now will help prepare you for when you finish school and go on to a job or college.
Six months may seem like a long time. But it seems to me to be about the amount of time you need to follow the recommendations I’ve made. If you are still suffering from significant OCD, you will no longer need your folks’ permission to make an appointment with a psychiatrist.
I wish you well.