Don't look at medication as some magic pill that will solve all your problems. You are too young to take meds for mental illness without significant oversight from your provider, and that should probably be a pediatric psychiatrist if that was necessary, not your regular doc, who isn't specially trained in treating mental illness. Not no training, but no special training. Treating the mental problems of people as young as you are is different from treating adults usually, as childhood mental problems are quite different than adult ones. They therefore need to be treated by professionals who know this and have experience treating it. You say you can't get therapy, but that's where we start when we have the kind of problems you are stating. Your brain isn't fully developed yet and won't be for several years, and the meds can be harmful because of that. Some your age definitely need them. It's best, however, to see if you can't fix things without them (that's usually true of adults as well). Medication also doesn't cure mental illness, we don't have a pill that does that, it reduces the symptoms so you can function better. Therapy, when it works, fixes the problem. Time sometimes also fixes the problem. I can't say what's really going on with you because modern medicine doesn't have that definitive answer, but from what you describe, you live in an abusive family, your parents are family and you love them because of that but you're also afraid of them with good reason, and so they have created a toxic environment for you. Religious zealotry if what you say is true and not just something you're projecting on them is also a brick wall to try to reason around. A therapist would be someone not related to you who will listen to you, let you have your say, and try to work out how you can be less insecure and depressed in a bad situation. There are ways of getting it that don't cost money, if you don't have it. But in your situation, you need an adult to advocate for you, and if your parents won't do that -- you don't say if you've discussed this with them or asked them for this kind of help and they refused or you only think they will refuse because you are projecting what you think they'll say without knowing this for sure because you haven't asked for help. The truth of the world isn't what we're propagandized about, as you've learned young -- family isn't a magic thing. Some are good, most are mixed, and some are awful. When you're young you're stuck with them unless you go to court and try to separate yourself from them, and that's hard. Your Dad seems to have learned a lesson about inflicting pain on loved ones -- have you tried talking to him about your Mom's behavior? You might not get anywhere, but you're stuck now so trying something is better. I would advise you to sit down with both your parents and in a nice and level way, without anger, say what's going on with you. Tell them you think therapy would be of benefit because if this continues you're scared what's going to happen. If that fails, do you have any other relatives who you trust? Do any of your friends have parents you admire who might help? Have you spoken to the school counselor about what's going on? Frankly, you're post is more articulate than almost every post on here, so I don't think you have an ability problem with school, so the problem would appear to lie elsewhere. As for siblings, heck, most of us don't get along with at least one of our siblings. My older brother was not a nice person, he had his own problems, but my sister was a nice person. It is what it is. Families aren't different than any other social situation, some of them we like and some of them we don't. And if you do manage to get into therapy, if your therapist does think you need medication, the therapist will refer you to a psychiatrist. It's not a decision you have to make by yourself and shouldn't make by yourself. When you're stuck, you gotta try something different, and when you're young, you have amazing resilience and ability to adapt far beyond what you realize now. Fix this now, don't let it fester until you're older. It's easier to fix now. Peace.
Boy, your post really breaks my heart. I am so very sorry it is so hard and you have little support if any from your parents. I can only offer that perhaps something that is a motivation for you is to do what you can to prepare to get the heck out of there. My son has been a long time anxiety sufferer and then became clinically depressed. He actually became suicidal. Treatment and medication have turned his life around but I am not sure these are options for you at all with what you are saying. Does your school have anything in place that can help? Some are better than others and I'm not sure where you live and what the rules are. For example, my kids high school has counselors but also a contract with a therapy center that comes to the school and will talk to kids. It's pretty universal in any large school district to have this with the suicide rates going higher and higher in teens. It's all free and done by grants. All you do at our school is make a request. So, it might be worth asking at school what could be available. However, I'd fear they tell your parents. You sound still very vulnerable to whatever their feelings are about right or wrong.
I want you to know that vulnerability to your parents is for a limited time. It WILL come to an end.
I'm going to give you this link to an app that perhaps you can get which is free. https://apps.apple.com/us/app/youper-self-guided-therapy/id1060691513 They have it on android too. But it is an interactive therapy app. Free. I have used it myself. It's 'something'. Feels like you are talking to someone and it is based in Cognitive Behavioral Therapy and Mindfullness principals. It's helpful, please give it a try if you can.
One thing we do with my son is work on small goals. When he activates the part of his brain that accomplishes something, even a small thing, it helps him feel better. What if you tried making a goal of say 2 things (they could be something like "today I will take a shower and I will read for 10 minutes". Start small like that. Build on it. See if that helps you at all. Keep in touch, I really really feel for you and the position you are in. This is So hard without any parental support.