I understand your closeness with your grandma & your feeling of loss for her.....even though she had been sick.
My daughter was in a very similar situation as you are now.....my mother (my daughters grand ma) died of cancer 6 years ago. My mom took care of my daughter most of her young life until she was in highschool. We worked & had our career, so our daughter went to grand ma's house & went there after the private school we had her in. My daughter was closer with grandma & grandpa than I ever was with them as my parents.....it was wonderful however because she got to know them & feel the wonderful love that was there.....that is something you will hold onto all your life with those memories & warm feelings when you think back to those times.
Grief takes quite awhile to get through.....take you time & feel your feelings.....they are all right for what you are going through.