Hi Serena,
You are one of the brave ones. Stephanie's advise to talk to the school counselor is a good one, and may be your best path for now. You don't have your age in your profile (smart by the way) but until you are eighteen your mom has quite a bit of control over what you can and cannot do.
Religious conviction is an almost bullet proof barrier to rational argument. Even if your mom gets the dysphoria, fear, and anguish, it will still be a huge leap for her to move past her well reinforced convictions to loving acceptance of your truth. I think that she is trying, and I think that she loves you. It is crazy hard to reconcile core beliefs with the reality of who you see as your son/daughter. I wish her compassion and acceptance, and you strength and endurance.
So let's say your school counselor can give you a referral to a gender specialist, or perhaps has some expertise there. The referral language of the letter to your doctor will reference the appropriate language from the transgender health standards of care (WPATH 7), but is neither complex nor long, your current counselor ought to be able to look up the language and make a referral. If there is hesitation, that might be something you need to talk to him/her about.
You are young and presumably healthy, so you don't need a specialist for HRT if your primary physician has some knowledge of transgender issues. That and periodic blood work to check endocrine and liver enzyme levels, is what you will need to begin the transition (along with a bunch of discipline and patience) at least for now.
OK, you have your letter, talked to your doctor now what? How do you get the support you need from your mom. In all honesty, I don't know. About half my family wrote me off as damned and has little to do with me. Their religion is a barrier to all argument and information. But your mom loves you, that might give you a chance. You'll need to know what you are talking about, show endless patience, and a develop a willingness to do baby steps. She will need to be able to see your feminine soul for what it is: beautiful, authentic, and honest. Maybe then?
Here is the thing. It may not be fair, but you have to be the adult here. You have to teach, advocate, learn, and be endlessly patient. I am here for you as are many others, but you are the bottom line for yourself. Gender dysphoria is chronic, and potentially life threatening, it must be eventually dealt with. Some of us lost decades before we became who we are - it can be done, but the cost is great.
Laura is right, "It is not the devil and there is nothing wrong with it." There is also nothing wrong with you. Let me know what I can do to help.
Julie