First of all, I am deeply sorry for your loss. Losing anyone is not easy, especially a parent.
Second, have you been to any kind of counseling? I would strongly suggest it for you.
I know you’re probably still in a state of shock and awe. It may take a while for it to really sink in that your dad is gone. Give yourself that time to heal. Sometimes people don’t deal with the hurt right away. Write a goodbye letter to him. Tell him everything you want to – maybe how you will miss him, special times you had, things you never got to tell him, say how you’re hurting. It may help to get that all out.
You may feel like you’re forgetting him because you aren’t crying, but you won’t forget him. The memories you have can’t be erased.