Very sorry to hear about your mom. I am going through the same thing as you, but about 6 months further along this life experience.
My vibrant healthy dad was just living his normal fun life. My mom found him dead in his tv chair, legs up reclined, watching tv, remote in his hand. She tried cpr too, but it was way too late. We all have / had PTSD. This was June of last year. They were supposed to come to my house that night for dinner.
I tried a lot of different things to feel better. it felt like I was looking over the edge of a cliff, jumping, then doing it over and over again. I also had to do what you are - managing my mom’s fright, I stayed at her house every night for almost 3 months, left my kids and husband at home every night. She was running around with friends constantly to escape, then we would meet up at her house. It was torture sadness disbelief - insanity. I still cant believe we made it through those early months.
When I wasnt with her, I would watch youtube videos to meditate and sleep.
The biggest help for me was to realize that I had to be more selfish and only do the minimum. I scaled down my work - couldnt concentrate anyway. Kids had to fend for themselves as much as possible. If I wanted to nap, I did. If I wanted a walk, I did it. This reduced a lot of extra responsibility and life stress.
It is important to take time for yourself and not pile things on that are hard to manage. Also, be sure to eat and hydrate. Grief is exhausting and no one really prepares you for that aspect. The stress and anxiety that you describe, are normal but its not normal to you because you have never felt like this before.
I can promise you that you will get through this. Its painful and not fun. Thats just what it is. But you will be you again. You will have peace of mind again. Your dad will feel better eventually. I think from hearing from other people and my own journey - that it can be a while for him. His life was just torn apart. Just being there for him is good enough. It will help build his inner strength.
One foot in front of the other…