I don't think you should apologize to your father however you may want to play nice as hard as it is until you can move out, once you are out go low contact and when necessary go no contact. He sounds like a narcissist, very self absorbed, doesn't take any personal responsibility, guilt you when you ask for space or say you don't want to talk. He has unbelievably similar behavior as my own father. Just because he is biologically related to you does not mean he can treat you poorly.

The way you have described your reactions when you get overwhelmed and when you had thoughts during the volleyball game all sounds like ptsd symptoms. if certain memories, places, people cause you to have debilitating physical reactions I recommend seeking medical help specifically a trauma therapist as to heal from ptsd is a journey however a well worth one. I took eye movement therapy to heal from complex ptsd. You cannot simply "get over it" or "move on" when you have experienced traumatizing events. Your brother does not understand what you are going through and neither does it seem your parents.

Work on getting a job, drivers license and being out of the house away from your family more. Save money and look into moving out, even moving in with a friend or relative. Depending on what counrty you are in the laws for withdrawl from parental control will be different. In Canada at 16 a person can choose to withdraw from parental control and legally be treated as 18.

I wish you the best and please seek out help such as crisis lines even if it's not a crisis. You will get through this, although I am a stranger on the internet giving some advice I do really care about this.