Frankly there are hundreds of badly injured kittens and we are least bothered about them. But if you really want to save this one, and be on time for your exam as well , you have got a few options.
One of them is that you can call someone from your family , your brother or sister or any other family member or a friend who doesn't have to appear for exam. Next option (a little less practical) is that you can pay someone around you telling them it's your kitten and needs to be taken to the hospital.
But if you really want to feel proud about something in life, your can save the life of this kitten by taking it to the hospital yourself putting your exams at stake. Yes, you'll be late for your exams, yes they won't believe your story ,but at the end of the day you won't regret doing this.