Death of a loved one or close friend is always difficult.
Breathe.
While you of course want to "be there" for your dad, and you will find ways to stay in touch and support him, this is something he and your mom were to work out and discuss...as adults... though it's often not done til the later years and death appears inevitable. Don't guilt trip yourself into becoming the companion for your dad now. But you both need each other and need to encourage each other to continue with life's activities.
Everyone grieves differently, so don't listen to anyone who insists this or that. Don't listen to those who say "just" in any of their sentences. You can't "just" when you are grieving deeply.
Know that it will lessen with time but how much time is totally your scenario.... there is no set time. BUT we all grieve. Some people appear to move with their lives without shedding a tear but eventually the known grieving sobs will hit them... it might take years.
For some of us it hits hard and long.... and we think it will never end. The Jews sit shiva... and then, if it was a spouse they lost, it's a year's process they give themselves to grieve.... but we never get totally over such a loss like a parent or spouse...
There are stages to grief, Kubler-Ross wrote about them long ago and they are still true.... but when we think stages we tend to think we go through this one first (shock denial) and then on to the next.... and then on to the next... nope. Each person grieves through the shock and denial, isolation, bargaining, depression and acceptance differently.
One day you might realize that you aren't sobbing at the mere thought of the loved one... and you feel you might be able to accept it and the next day you might be so depressed you can't function. Some days you might experience all five!
Keep moving forward.... try not to let it control your life (your loved one wouldn't want that either, and I believe they can see/hear us here)... don't constantly fight the grief. If you can take a set time (you decide how long you need) and sit or walk and think about the person, focus on the good and the not so pretty stuff about them, then stop and put the memories back on the shelf to take down again later.... you might find that you are beginning to control your grief. I would caution to not just think about all the good stuff about the person... no one is perfect... to grasp reality and help ease the grief you do need to begin to recall the bad attitudes or absolutely dumb things she may have done. (Such as my mom used to chase everyone out of the hot kitchen where she had baked something and had the oven door open, "so the oven can cool off". She was 80 before she realized how dumb that was!)
Most people aren't around their parents alot when they are adults...and the sense of having a parent is mainly in the mind at those times. For me it was/is the "oh I'm want to call mom and tell her..." moments that hit hard knowing that while she's always there in my mind and memories, she isn't there to call.
My mother will have passed 8 years ago this May and while I talk to her a lot some days I just. plain. miss. her.
Be gentle with yourself and don't rush. If you want to talk to someone, then do so but find someone trained in grief support as I would hate for you to be told something that makes the teller feel better and doesn't help you cope with your loss.
https://psychcentral.com/lib/the-5-stages-of-loss-and-grief/
