Thanks for your post. I'm sorry to hear about your Nan. It sounds like it's been really hard on you.
It's totally understandable that this is overwhelming you at work. I'm guessing that your head is probably full of grief at the moment and yet work is asking you to push it all aside and focus? Is there anyone that you've talked to at work who can support you at this time?
It's a great idea to go to the gym. Are there any other ways that might help you cope? Or would it help to try and feel close to your Nan? While it doesn't work for everyone of course, sometimes it can be really therapeutic to take some time and look through photos or find ways to feel connected with her. I know for me personally I had to find this time to just get absorbed in my grief so that it didn't turn into all this overwhelm. Maybe that could be the same for you.