OP, remember that different people cope in different ways.
I think a lot of people put too much emphasis on how you grieve. If you don't cry your eyes out, spill it out to someone, it's okay. The death of a loved one is something extremely personal, and it's okay not to share your pain with others.
Having said that, sweeping something like that under the rug and forgetting about it is not the best way to handle things. Remembering who you lost is extremely important.
I lost my dad on Dec. 6th, 2012. We were over at my grandmother's house, I think I was reading through some magazines in that moment, when I heard a thump coming from his room. I ran to him and tried to keep him breathing and stop the bleeding from his head (turns out he had a brain hemorrhage), but by the time the ambulance arrived, he was already dead. Seeing my dad die in front of my very eyes and being unable to do a thing about it was pretty jarring.
I was very shocked until the ambulance arrived, at which point I calmed down. The next day I was already cracking jokes. My family thinks I'm heartless, but you see, as I said before, different people grieve in different ways. My grandma (my dad's mother) didn't cry, but she did feel depressed and mostly refuses to go out of her home. My mother fell into deep depression and was unable to function on her own for a while. My older brother was a bit down for the first few weeks, and then went back to normal.
But here's the interesting thing. All of us, even though our immediate reactions were extremely different, have our own way of remembering him. My mother still keeps all of his CDs and vinyls, my grandma has his broken glasses in her purse and his empty wallet, my brother has his old PC and all of his files saved on external hard drives and cloud storage, and I have his old cellphone (yes, I pay his mobile plan and the phone still works) and a few old videos and pictures of him.
When I feel a bit down, I read some of his old texts (there's one that I particularly like, where he tells my mom how proud he is of me), and when I accomplish something (e.g. when I scored 91/100 on my FCE exam, or got accepted into college) I send him a text. When I think I'm forgetting what his voice sounds like, I listen to his answering machine or to those videos.
Sorry for being kind of all over the place. I guess what I'm trying to say is it's okay not to spill your guts out to someone. But I don't think it's a good move to pretend nothing ever happened and nothing was lost, because it couldn't be any more different from that.
This person is gone but not forgotten. Honor their memory and honor what they meant to you as a person and how important your friendship/relationship was.
Having said this, I'd like to say I'm very sorry for your loss and I know how tough it can be. I wish you the very best in the aftermath of what happened, OP.