Edit: He passed away a few hours in front of me after I wrote this post.
Sorry for your loss. It'll be hard, but try to draw strength from supporting your Mum... and let her support you too. Being needed can be a great source of comfort, as can allowing others to help you when you're at a low ebb.
There are no rules for grief, though the "supportive" nature of the necessary arrangements can be a framework which forces you through the first few weeks and helps a little. But don't be afraid to make it up as you go along and do
whatever helps you cope, no matter how daft.
For me, with no other family commitments and some savings to buffer me before I have to get a job after 8 years of caring, it's been walking since dementia finally killed my Mum in November. Perhaps don't aim for 50 miles a week (at least I'm down from 75 the first few weeks!) but... getting out, fresh air, random chats with strangers (many of whom will be entirely familiar with grief's sledgehammer). I can also recommend -- perhaps not in these early stages, but later, when support starts to dissipate and things can get harder in some ways -- Cariad Lloyd's Greifcast
podcast and perhaps the recently release
book for your Mum.
I listened to Rev Richard Coles' "The Madness of Grief"
audiobook on an Audible trial straight after Mum's death. His experience wasn't too similar to ours, but the journey and "madness" is the same for all in many ways. It was a comfort to hear his.
I'm not going to say it gets better quickly. It doesn't. Two and a half months on I'd say my life's only a complete mess rather than a total mess! You've lost one of very few witnesses to every moment of your life, and someone who knew you almost, or maybe even better than you know yourself. Grief is, as the tired old cliché goes, the price we pay for love, but it's a terrible price.
The very best to you and your Mum, and to all those out there who may read this at some point in the future, seeking some kind of solace or support at their lowest ebb. I have no Faith to lean on, but as an anti-social, Billy No Mates type for most of my life, I've learned that there are some things human beings are simply not meant to, and probably not capable of, dealing with on their own. Meet, talk, read, share, type frustrations into the great social media void; do whatever you need to do to get from one day to the next and be the person your Dad would want you to be. He can't hug you any more, but he helped make you what you are. He's still proud of you; he just can't tell you.
Where's the hug emoji when you need it? Made myself cry just typing all this. Which may be why I'm irrationally sharing what I wrote for Mum's small graveside service.
Love isn't measured in flowers
Love isn't measured in grief
Love isn't measured in years
Or in a sense of relief
Suffering may be over
Mourning may begin
But love isn't measured in tears
Or in a gathering of kin
Love survives
Our rise & fall
And love can't be measured
...at all