I (16f) accidentally made my dad (45m) cry during our huge fight. What should I do?

We fought about my older brother Matt. My dad and him have always fought even when we were kids and it has caused A LOT of tension in this family (there's 3 of us). Their personalities clash a lot and they are both very very stubborn strong-headed people. My dad is a CEO who can be controlling and an ******* and Matt sometimes does stupid stuff on purpose. I am close with both Matt and my dad but it is so tiring being in the middle of so much conflict and fighting.
Matt is going to college in a few weeks. Tonight my dad and him got in a fight over something. I don't even know what. There was so much yelling and shouting and Matt ended up packing his bag and is now staying at his friend's house until his school starts. His friend lives over 45 min away so I probably won't even get to see him again or say goodbye or hang out. I feel heartbroken.
I'm angry at my dad for all of this. I know this is unfair but honestly, Matt is leaving in a few weeks for college and I am extremely angry that my dad had to be such an ******* and couldn't just be nice to him for a few weeks more. I'm also just angry that he has been so hard on Matt our whole lives and can't just let small things go, he could have been a much better dad to Matt and there would have been less fighting and conflict in this family.
Well I started yelling at my dad and defended Matt. I said some things I 50% mean 50% didn't mean. My dad started crying and then he left to go for a walk and is now in his bedroom. He left before I could apologize for some of the terrible things I said and when he came back we didn't talk.
I feel very overwhelmed and emotional right now and I don't know what I'm supposed to do now. My friend said I need to go to my dad's room and apologize to him for saying some things that were completely out of line. But I'm angry still at him and feel conflicted.
tldr; My brother and dad got in a big fight that resulted in my brother leaving the house. My dad and I started fighting and I said some unfair things that I shouldn't have said. What do I do now?


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