Hannah,
You will always be their grandaughter, even though your grandparents are no longer around.
Your feelings are completely natural. However much we try to prepare ourselves, death always comes as a shock to us as it is so final and any threads of hope we may have had are finally gone. Allow yourself time to grieve and remember that whatever you are feeling your Mum will be feeling the same if not worse. Support each other as best as you can and make allowances for the fact that you are both grieving.
Meanwhile, try your best to remember the good times with your Nan and the way she was when you were both younger and times were happier.
I hope you and your Mum get through the coming weeks OK.
Dave
x