You are not being a big baby. From what you wrote, I don’t see that you are a bad daughter so much as a normal 14-year-old who is beginning to want more independence.
Let me be perfectly clear: Parents do not have the right to beat their children — ever. They do have the right to be unreasonable and to set rules you don’t like. But they don’t have the right to hit you and to make you so scared of them that you are having anxiety.
Please talk to your school nurse or school counselor or a teacher or another adult you trust about what is going on. Your parents need help learning how to parent a teen without resorting to violence. It is likely that they will only accept that help if another adult talks to them.
I wish you well.