I'm sorry to hear this, Scarlett. It must have been a huge shock.
Dont try and put a time on grief. Tbh it is very early days yet anyway. Grief manifests itself in different ways and different people respond differently. Do not ask too much of yourself and accept that it is OK not to cope.
In time you might find reading the Cruse website helpful. I know I did when Mr BM saw his dad die in rather horrid circumstances and grief had a real and lasting effect on him.
https://www.cruse.org.uk/get-help/about-grief
And I am sorry to say, I do not believe time heals. I believe that time helps us adjust and accept but that wound will always be there to some extent.