I’m very glad you wrote. Many people are under the impression that a diagnosis of OCD requires both obsessions and compensatory compulsions. That simply is not the case. Yes, it is possible to have OCD with only the intrusive thoughts. And those thoughts can include the additional intrusive thought that you’re faking it.
One of the characteristics of true OCD is that the sufferer is aware that the thoughts are irrational. But the person can’t “reason” themselves out of them.
If that is the case for you, I hope you will talk to a counselor who specializes in OCD. The good news is that OCD can be managed, usually by a combination of medication (at least at first) and coaching in “thought stopping” and other techniques.
I’m sorry you don’t feel you can talk with your family about the problem. Maybe it would help if you showed them your letter and my response. Or maybe it would help to talk to a school counselor or another adult you trust who can then talk to your parents. Sometimes parents are more likely to listen to another adult they respect.
I wish you well.