I know you had to defend yourself, but the right thing to do was go to your room to calm down and tell your grandma your feelings when mom isn't nearby. Pulling her hair made it even worse. Mothers like that are just stressed about their busy life. When it's a good time just tell her that "it must be hard for you, but I'm sorry if I did anything wrong." something like that maybe. Do more for her, like help her with cleaning the house, etc. If your grandma gets confused about what you said earlier, then explain it to her. It was bad of your mom to treat you that way, she should've took a second to calm down her frustration, but moms might have a hard life as well. Or if your grandma is trying to explain about what you did wrong, just tell her you understand, and you were just frustrated like your mom. Since you said your mom does this to your siblings then tell them how you feel as well, and tell them that your mom is just stressed out. If your just scared to tell your sisters and brothers then don't talk about "mom is having a bad life". If your siblings are fighting with your mom try to stand up.
You will find a way how. If one of them shouts at you, it's okay because you have to have that kind of experience if you want a nice future. Also, the reason why your mom isn't being mean to your baby brother is because she doesn't want, like when babies see their parents shouting at them, they cry and when they cry, your mom has to try to quiet him down, and she's too busy to do that, but your right, if she can manage her frustration with the baby then she can manage her frustrating with you. Another thing, your mom can't spoil you, she has to set a few rules, and sometimes get strict so you can follow her rules but she shouldn't tell you not to cry, or threaten you that you'll get hit. So that's all I got. Tell me if you need anything else, and just for you to know. No offense to that "I know you had to defend yourself, but the right thing to do..pulling her hair made it even worse". Just like your mom was angry because of something, I was angry when I thought about why a mother would do that. I just like have some experience with being a daughter. And again, I'm sorry about your mom and I understand how you feel.