If you are going to write a short story, you don't need to make things up entirely.
You should always use as much creativity as you can, but you can also take elements from real life and incorporate it in your story.
No, students shouldn't be allowed to have pets at school. Though many students love the thought of pets by their sides, it can be a distraction and many students that have allergies to pets. Imagine sitting in a classroom taking a test, and pets start going crazy, barking or causing a scene. Or students rubbing their eyes or sneezing at the shedding of fur. Students could also start playing with their pets and become distratced from their teachers. In conclusion, students may love pets at their side and may think it would be better, but in the end it would be a pretty bad idea.