Big big hugs OP. My dog is 11 and was very ill last year and I thought I was going to lose him. I don't think I have ever cried as much. I spent hours and hours reading and researching trying to find things that would help. It was a blur of a 6 months and I remember praying to god (I'm not religious) that if I could just have him stay with me I'd never ask for anything ever again.
I lost my mum the year before and my dad 5 years before that and the prospect of losing dog was I think the worst.
As you say you don't want another dog you want your dog with their funny little habits and ways. They know the routines and you have your own little communication system.
Mine has been with me through a bad breakup, job losses, moving houses, 2 deaths and is my only remaining family. I utterly, utterly dread him going. My world will stop.
Thankfully after specialist care he has recovered although he still lives with an ongoing condition. He also has a heart murmur now. My whole life revolves around him. That sounds crazy but it's true. That's not to say I don't do other stuff too but I've always got one eye on the clock (when is next walkies, when is his dinner due, when is his next groomer appointment, what toys and games can I use to keep him busy in the house).
When he was ill I tried to make myself think about getting another dog and I felt literally sick at the idea not to mention guilty.
I guess going through the grieving process and just taking it day by day (or minute by minute) is all you can do.
Someone once said to me try and be happy that you had them, rather than be sad that they are no longer around.
From one dog owner to another I hope your grief is bearable until you heal.
They are darling furry angels sent from heaven to make us laugh and make our life bearable.