I’m most concerned that you believe your mother would think you are trying for attention if you shared your story with her. Of course, there is no way for me to know whether you really aren’t getting enough attention or if your beliefs about how much a person should get is unrealistic. That being said: Is it possible that you are upping the seriousness of your thoughts in order to get the attention you need?
In itself, the incident with the bird doesn’t worry me. Little kids sometimes do horrible things out of curiosity or ignorance. But the way you remember it does worry me a lot. It looks to me that you are projecting your current angry feelings about helplessness onto that event. Is it possible that you hate how helpless you feel? In addition, you report symptoms that do suggest Obsessive-Compulsive Disorder. If that is the case, it could be that the OCD extends to your thoughts as well as behaviors and that you can’t easily let go of an idea once it takes hold.
These are complicated issues. Your letter is very articulate for a 13-year-old. That tells me that you would benefit from seeing a counselor to help you sort them out. I hope you will show your letter and this response to your mother. Some sessions with a counselor who specializes in working with anxiety disorders and teens would help you manage your symptoms and give you peace of mind.
I wish you well.