My problem is that I shut down at times like this. It's a struggle to do anything.
It's called dissociative. It's that out-of-body feeling, going numb you have.
It's the mind's way of protecting itself when you are experiencing something so big, so awful and so traumatic that it becomes too much to deal with. The feelings are way too big to process in the here and now.
It's sort of a mental credit card. You are feeling some pretty big things right now, this is a hugely painful experience. I would encourage you that when you feel sad or mad or glad or whatever, then give yourself permission to feel it. Otherwise those feelings stay bottled up and that's unhealthy.
It's encouraging you cried. That is a healthy, normal and natural reaction to what you're experiencing.
I would also encourage you to say whatever you need to say to your father before it's too late. I did that with my mother and although it did not come out right (I cringe now when I read the letter I wrote her), I'm glad I said it before she was gone.
If you need to talk, you know where Nina and I are.
Be well my friend,