I don’t know if you have a personality disorder. Most teens go through periods of thinking and acting in ways similar to what you describe as they work on figuring out who they are. Most teens suffer from doubts about their self-esteem at one time or another.
What concerns me more is that you apparently didn’t get a mental health evaluation and treatment when you cut yourself so deeply. You have presented a very complicated picture of yourself. Your letter also shows me that you think hard about things and that you would do well in the give and take of an honest conversation with a therapist.
I don’t have enough information to give you a responsible response to your question. I encourage you to do for yourself what was not done for you when you were in the emergency room. Make an appointment with a therapist. Bring this letter to your first appointment as it will jumpstart your conversation. You deserve to get your symptoms and your apparent double life sorted out. If you could have figured it out on your own, someone as bright as you are would have done so already.
I wish you well.