I am so sorry about the death of your Dad. You have been through a traumatic experience and you need to give yourself time to process what has happened and come to terms with it.
My Mum died, suddenly, 3 years ago and I was unable to get there to say goodbye as it happened so quickly and without warning. My Brother and I had to push our own grief aside to help our Dad try to process the loss of his wife and deal with all his emotions and his awful grief where, at his lowest point, he wanted to give up. It has been the worst 3 years of my life and I needed therapy to come to terms with what had happened and the massive change in dynamic it brought to our family as Mum was literally the glue that held us together. I had to deal with my own guilt for not being there when she died.
I sympathise with you having to deal with the remaining parent, its so incredibly hard but don't do what I did and push aside your own grief by trying to be strong for everyone else. It caused me to crash and burn but my therapist helped me through it and helped me deal with the trauma and guilt and thankfully I have come out the other side. I am finally now able to think of my Mum and feel immense gratitude for the fact she was my Mum and for everything she brought to mine and my daughters lives. But it has taken time to get here and for the sadness to turn into that gratitude. I can now think of her without feeling such immense sadness and trauma and I now think of her and smile, rather than cry.
Losing a parent sucks big time and you will never ever stop missing them but I promise you that it will feel better, even though right now you probably don't believe that.
Sending you hugs xx