I am really sorry that this happened to you. The longer you are in the field, the more likely it will be to happen.
Take a deep breath. You are a student, and while you are there to learn and practice, it is the responsibility of those who are training you to give you tasks that are appropriate to your skill, and to oversee your work. It is very hard, when you’re learning, to know exactly what you don’t know. I don’t say this to absolve you of responsibility, but to remind you that you are not expected to be alone in this right now. Any error that lead to the fatality in this case is an error that the team is responsible for, not just you.
In the short term, reflect on what happened - did you make a specific mistake? If so; why do you think you made a mistake? Were you rushing, did you feel pressured to do something before you felt ready, were you overtired, were you overconfident? Approach the veterinarians who you were working with and ask to reflect on the situation together. Be honest. Tell them that you can’t shake the feeling that you were at fault for what went wrong. Let them explain to you why they think that isn’t the case.
In the long-term, do everything you can to avoid accidents - and by that I mean, errors in math, grabbing the wrong product from a shelf, forgetting to check your anesthetic machine, etc. Be thorough and careful. Part of that is making sure you sleep and eat. Part of that is making sure you do not let anyone rush you into skipping protocols. If you need to, have someone else check your calculations for important drugs - there’s no shame in doing that, everyone can make a human error and type something incorrectly into a calculator. I ask my techs to look over my math all the time. It’s not because I can’t do it, it’s because one number error in our job can have real consequences.
As for true errors in medical judgement - you, just like everyone, will eventually be faced with cases that exceed your medical knowledge. Learn to identify those cases, step back, and ask for help if you need it. Plan ahead as best as you can. Go verify something before you start. The majority of your cases will be fine if you take another 5 minutes to think.
There will be some situations you encounter where you have no choice but to make a split second decision (your patient is hemorrhaging, seizing, etc). Do your best; in some of these cases, it is you or nothing. If it turns out that you cannot save the patient, console yourself with the fact that the patient passed /despite/ your best efforts, not that you failed or that you are at fault. Don’t get into the habit of thinking, Dr. So-and-so would have done a better job than me - if that person wasn’t there, then it’s a moot point.
Edited to add - and when you do all that, and you still face a situation where you did something wrong and a patient died: be honest with yourself and with the client. Explain what happened. Apologize, if the error is something that was truly preventable. Then take time for yourself to cry and be frustrated. Recognize that you are a human being, that you are not infallible. If there is anything you can take from the situation to learn from, then do so. It is an unfortunate reality of the profession, and the most you can do is to truly give each patient your best.
