May I offer my condolences OP?
My DH died suddenly last year too, and I felt numb for a month. ScottBakula's post is comprehensive and very helpful.
For others reading though, there are things which need to be pointed out - an inquest and a post mortem are two different things. We needed a PM for my husband because he'd died suddenly at home and hadn't seen a GP for some years so she couldn't certify his death. We didn't need an Inquest because they, ( and I am not sure who they is) was able to say that it was due to natural causes.
The coroner issued us with about 10 interim death certificates and most organisations accepted these, so although I paid for 5 death certificates, in practice 2 or at most three would have been sufficient.
The funeral directors dealt with his body and liaised with the hospital and Coroner and again, like the coroners office, the people involved deal with bereaved people all the time and are helpful and know how to offer comfort to people.
I personally found that doing all the admin that was necessary was helpful to me, but others might not. Each of us grieves in our own way.
Since then I have found going to other funerals have been particularly difficult and maybe surprisingly weddings also.
But I can only say, take it one day at a time. Bereavement to me is a journey which I would rather not be taking right now, but I have no choice.