Bf punch me after i threw water at him, all my fault?

My bf picked me and our baby up (we don't live together) from my house and when I went to his car he was in the passenger side n he told me I was going to drive today. I told him I didn't feel comfortable because I'm still learning and I was scared since this would be the first time driving with our 1 half month old baby. He bitched at me saying I will never learn if I make excuses so after arguing for a while I just gave up. The whole time he was giving me attitude, I was making wrong turns, slowing down a lot, speeding, etc. He was making me more anxious and I told him I was scared and wanted to stop. When I tried pulling up at his driveway I completely fucked up and he told me to reverse and I asked him if we can switch seats cus at this point cars were passing by and I didn't know what to do. He said no and bitched again. I stepped out the car and tried to get the baby out and he called me crazy for "putting our baby in danger" and he took over to park. When we got inside he kept bitching and bitching and I started crying because I had so much anxiety. I told him he was an asshole and that I wanted to leave. He then said to leave and I asked him to drive me back home and he said no so I got mad and started to pack up the baby's stuff again then the baby started crying and he picked her up n called me a bad mother. I asked again to be dropped off and he said no. He said if I wanted to leave to find my way back home. So I called an uber and told him I didn't have money to waste on a 20 dollar ride and that I was upset, at this point I was really angry since he knows I am currently not working and tight on bills. He said it was my fault and when I tried to ask for the baby he said no then claim that I can leave but the baby was staying. I called him crazy and tried to take the baby at this point he's walking away across his room with the baby. I asked again for the baby and he said it was not only my daughter and that I was selfish and to leave on my own. I started crying and shouting at him that I wanted to leave already and my uber was going to charge me if I don't go (which it did). I told him I was going to call my dad and he laughed and said he still wasn't going to give me the baby. After 10 min of this I tell him I was going to call the cops. That I didn't want to but he was giving me no choice and he laughed again and said the cops wouldn't do shit since he's the father and will actually tell me to leave then I reminded him that he wasn't on the birth certificate so technically he has no rights. He then told me to call the cops and I really didn't want to do that to him and I was angry and crying that I grabbed the baby's water and threw it at him. Which then he pounded my head and I grabbed my frappe and threw it at him as well he bloked it and it ended up splattering the room, on his couch, floor and on my self. Then he punched me again twice on the head and I fell on the floor not being able to breath. I kept breathing hard and got a panic attack then threw up. He started calling me crazy and he ended up hitting me again and twisting my arm because I hit his side and pulled his shirt. He said all this was my fault and I caused all this. He's a 6'ft guy and weighs about 250 and I know hitting is wrong but my punches or shoves are nothing against him and I never hit him in the face or head. I started bleeding on my nose a bit even tho he didn't hit my nose and I felt really light headed. After a while of fighting he tells me to calm down and I begged him to just leave me alone and take the baby back home. I kept asking to hold her which then he gave me the baby then asked to "talk" and I was in disbelief. He then said "whats wrong with you today what's going on"? Like if something was wrong with ME? I cried and told him I didn't want to be with him.no more. I feel bad for my baby and I asked for us to stop fighting because of her n he started being manipulating now I can't help to feel like it really was my fault for hitting him with the water bottle..this is not the first time he's hit me. While I was pregnant he punched my head while we were arguing.