Saying that it’s “just something that happens,” suggests, that she is aware that she sometimes loses control of her emotions. It sounds like she really does need therapy, and maybe medication as well, but denies that she has any need of it. So, you and your dad are dealing with someone who can’t control her emotional outbursts, but doesn’t see that as a problem. It may well not be a problem for her, because she is not at the receiving end of the blowups.
It’s very clear that her blowups are not the result of sound judgment or perception. Therefore, whatever horrible things she says to you are, in all probability the result of mental/emotional instability. It’s hard for a kid to accept being treated that way by a parent, without fearing there is some truth to whatever offensive thing the parent is saying. It’s even worse when a parent won’t admit to being wrong about treating their kid that way. Keep in mind, her bad behavior is 100% her issue, and is absolutely no reflection on you. It’s very common for parents to disrespect their children, while expecting respect in return. Parents who disrespect their children are deficient in parenting skills and blaming their children for it.
You might as well try to get along with her as best you can. Regardless of what she’s dealing with mentally, she must be convinced that she’s doing the best that she can. A very good practice that will serve you well, now and for the rest of your life, is to remain calm and genuinely respectful, even towards those who are acting like idiots or mentally unbalanced. I know it sounds like a tall order, but it’s doable.
Besides, your mom’s yelling is essentially made up of soundwaves. They cannot break your bones. They can’t change the truth of who you are, which is a decent and pleasant person. It may not feel like it, but you can consciously choose your reaction while she is yelling. You can keep your own thoughts calm. You can let her wear herself out with her venting. Then when she has calmed down, maybe the two of you can communicate thoughtfully. My mother was pretty crazy. She threw huge tantrums, and sometimes could keep them going for a couple of hours. She was very delusional, bipolar, schizophrenic, and I’m fairly certain she also had borderline personality disorder. However, as crazy as she was, after her tantrum ran its course, our communications could be surprisingly rational and calm. By the way, she went to her grave, never having admitted to any mental or emotional problems, and was convinced that she was never wrong about anything.
Regarding self-harm, you’ve made it 348 days. Congratulations! Can you make it just one more day? Stress in your life is triggering the urge. Odds are, you have dealt with other stressful triggers in the past year. How have you dealt with them? It may help to acknowledge the urge without being afraid of it. When we talk about fighting something or struggling with it, you are giving it undeserved power and influence. Instead, “turn away” from the urge, and choose a different way of dealing with the stress. You’ve already done that countless times, and have proven that the urge doesn’t have the power to control you.
You speak of having to work through trauma. That’s a good idea. Get help if you need it. It will make other challenges in your life easier to manage.