Everything about your post is right, and I would possibly say somewhat more controlled and accepting than some people, if this is the first time you have lost someone close to you.
As you probably know everyone accepts these events differently but if I tell you how I get passed difficult times maybe you will find it useful.
As I see it, when we are born we are pretty much 'nothing' as a person but it is the people around us who make us who we are. Your Grandmother obviously played a big role in this and had a lot of influence on who you are today, she helped you to start finding a place in the world through teaching you (although it never seems like teaching). As long as you remember the times you were with her, remember the things that she told you then you can make sure that no moment was wasted.
I will accept, even at the age of 18, I am a small person in a large world, I have little experience, but thankfully, older people I know have shared some of their experience to make it easier for me. It sounds as if your Grandmother has done much the same for you.
So I say you should go tomorrow, but don't see it as a sad occasion (as difficult as that may be), but instead be thankful for who you have become and show that you can pass the final 'test' where you remember what you have been told and use it without support.
Having said all that, don't expect that to solve all the problems, but in time that feeling can replace the feeling of loss. It takes time, but cycling through those thoughts everytime you feel down, it will slowly make sense and become a part of you.