Hi.....so sorry for your loss such a great one for you and so suddenly too. What you are going through is pretty much normal.....I lost my mom about 9 months ago and my brother 9 months before that. And I still find myself aching to talk to them by phone and see them again.
It does get better each day......in the beginning I was much like you, it felt as if the world was spinning around me and I was just there, numb like you describe.
As the days went by I learned to smile along with the sadness, remembering the things they did and said which would warm my heart.
The memories you have of your dad will carry you through the grief, for they are yours to keep forever.
And eventually you will join in with life again and see it in a different way, carrying your dad with you in your heart each day, honoring him by living it the way he would want you to.
So, give yourself permission to mourn your loss for it is a great one to lose a parent.
And then commit yourself to getting back into doing the things that would make your dad proud. As you do you will find a new way to have him in your life and see his presence in a different way.
It sometimes helps to keep a journal in which you can write to your dad telling him how you feel....and as you do you will move forward and find it to be easier to bear the loss.
Sending you some (((HUGS))) and understanding your sadness.