A book isn't just written by the author to tell the reader a story. It has a narrator. The narrator is not the author. Even if there is no narrative frame in which the narrator of the story is made explicit. The narrator is a function of the narrative, just like plot or setting or character. It is never a real person, even in an autobiography. The narrator is a voice whose style of narration is chosen by the author in relation to the story, to effect a certain "feel".
For example, it is the narrator which makes a story humorous or earnest. Think of a friend telling you how he had to undergo a painful medical procedure. He can tell the same events to you in a way that you get a good laugh at his expense; or he can tell them with a focus on how bad it all felt and cause you to feel compassion and tenderness for him; or he can choose a more neutral style, considering the interesting advances of medical science. The story does not change, only the narrator does. And it changes with the choice of words, of grammar, of the linguistic register, and so on.
A narrator that uses contractions will maybe evoke a feeling of a more immediate, verbal narrative style, of being told something by someone, of a witness of the events, while a style without contractions might feel more distanced, more objective, less involved. Of course the use or disuse of contractions alone is not enough to have that effect, but it will be part of a narrative strategy that will put the reader in a certain frame of mind and thus help the story evoke the emotions in the reader that the author is aiming for.
From all this it should become apparent that it must be your choice how you want to narrate your story. There is no right or wrong, only your artistic vision. If you feel unsure, you may need to experiment and learn the proper use of your tools.