I have serious problels with my dad

My dad has serious nervous and anger issues. For as long as Ican remember he's been yelling horribly at my mum for mundane things (because her tight has a little hole and such). He yells at me everytime. For little things. Imagine when I do something slightly overboard. For exemple I had once a dog who peed on the floor, it wasn't my fault I was 12 and even I took the dog out he didn't get that he shouldn't pee in the house. First I thought it was some water so I told him so, when I saw that it wasn't I said that I was sorry that I took him for a walk. But he kept yelling and at some point he grabbed me by my neck made me put my nose in the dog's pee to "see if it is water" . I'm fifteen right now and I'm livong with him and my grandma. He is often really nice, he cares a lot for me and gives me everything I may want or need. But his anger issues affects me too much. I get anxious. I stress when he's calling me on the phone or just calling me over. When he shouts at me I usually can't control muself, I start crying, and he keeps yelling at me, insulting me, criticizing me and looking at me with a disguste face. When my hands start shaking he gets even more mad, he mays hit me on the hands even though I really can't control my shakings even if I try to. Sometimes he hits me but it's been a few months already he hasn't. But he did it often when I was a child, he didn't just slap me, he would throw me, grab me by my neck, grab my hair, He even used to sometimes hit mum. He usuallt regrets his anger a few hours later the conflict and tells me that he didn't want to shout but that I'm still wrong. I can't really get mad at him because he truly cares for me but I really can't take it. Just thinking about him shouting at me at any time of the day makes me cry. Even now. It happens so often. It's not just once in a while. When a teachers or a friend slightly raise his/her voice at me I can't control myself. I feel a knot in my stomach and feel dizzy. If it goes on I start crying. Over such non important things. It affects my life I can see it. But I do not know how to react. Am I wrong to feel like that? Should I be trying to be more understanding? But I really try to I've just reached my limits. Thank you so much for reading that and even more thanks for the advice you give me.

Thank you for answering. My grandma usually tries to calm him down but there isn't much she can do. I don't really know who I can ask for help, at the same time I don't want to create legislative issues to my dad. At some point I wanted to tell my mum but she's abroad with my sister and I don't wan to create her worries. I don't want to put her in a situation where she has to face my dad.