My dad and me had a huge fight I called him names help me?

Well here is how our fight started. I was home alone and I went outside to check on the hens to see if they were ok. And well I have a little dog called Minne and she is not aloud outside when my parents arent' around because she trys' to escape on to the road when they are not here at home. And anyway right as I was heading back into the house I thought I seen the dog run up to the gate go underneath it and run out on to the road. Then after about a minute of that happening my parents came home I told my dad what had happened he then went looking for her. Then 5 minutes later my brother found the dog inside the house it turned out she hadn't' run away at all. Then my dad went ballistic at me and started getting really angry by saying ah amy what are you doing I then said to him I could have sworn I had see her at the gate go out. Then as I started walking away inside my dad started shouting at me and getting really pissed off at me saying he had to go looking for her I then shouted back at him that he was self righteous because I felt he was going me too hard a time for making a mistake. I then shouted inside to myself that he was a ******* prick he unfortunately heard this and then when I was on the stares trying to run up to my bedroom to try and avoid him he caught me and said don't' talk to your father like that you will leave this house I then screamed at him your a ******* prick and that you give everyone a hard time over making a mistake and then when you make mistakes you dismiss all responsibility. I then went inside my bedroom. I got so angry at him because he was giving me such a hard time about it and wouldn't leave me alone. I mean people makes mistakes right even my brother said he totality overreacted.Perhaps I shouldn't' have called him names but he was way too hard on me and what I said about the mistake thing is true and Im now hiding in my bedroom how can I solve this. I cant' keep hiding away. Im sorry for the bad grammar and spelling I cant help that. I know I shouldnt' have got so mad either its just he wouldnt' shut up and let me calm down and leave me alone.