Just come back to the forum after a break . So very sorry to hear your dad has died. Mine died 29 years ago and just the other day I was driving to see my mum (she is the one with Parkinsons) in her nursing home and I got quite tearful wishing he was still around to take care of us all like he used to. I am nearly 57 by the way!
I think father's can be very much underestimated and when they go it is major. Many, perhaps most, dads are an anchor in life, even when they are ill or not around much for a long time. When that anchor goes, we are left adrift.
You are now still in the worst part of grieving. It does get better. After a few days, then weeks, then months you will wake up and think, Oh, it's starting to get easier. This is grief and very human. You will learn about yourself through it and later, when the process of healing is further on, you will realise that if you can get through that then you are stronger than you thought you were. Think of it as one of dad's last great gifts to you: giving you the strength to know that things can be really bad but you can get through and he will always be there as an invisible support.
Your mum needs you to keep it together. Another of life's great lessons: we often have to be our parent's parent. Everyone is different and you will both get through it together in your own ways. You are lucky to have your mum and you will be able to support each other over the grief. Maybe this will bring your relationship with her to progress as well.
Deepest sympathy. Accept any help people offer you. When my dad died I wanted to talk about him but no-one asked. I remember that. Talking might not help you but if you think it will, take advantage of chances to talk about him and how you feel. Probably not necessarily with your mum as she will need her own support. If you can, treat yourself to things you like. Last advice: don't feel guilty if you stop feeling sad for a minute or more. That will be dad helping you feel better and the grief healing.
All best wishes, The Choogler