(((hugs)))

I think you might be overthinking on this.
You seem to have things figured out on one hand, yet you project a strong feeling like you NEED to tell them. Why? You are certainly "on your own" so much, do you get permission for all of your decisions? Why can't you get your own bank account? Or a savings account you can write checks with? Why would they be upset that you're in therapy? Wouldn't that be their issue?

Your self harming behavior is a symptom of other issues...not a disorder in itself. Once you begin to work through some things that are bottled up in you, that will ease. Perhaps some of the other issues will too? Why not give therapy a try. BTW, there are plenty of Christians and other religious people who do well in therapy, and there are many Christian therapists who stay in business with ease. If your folks do find out and give you grief over it, tell them that God uses doctors to help people all the time!

TC of yourself first. Then you can help others too.