There was no pulse--there was no breathing; amid the silence of my patient's body, there was chaos all round.
This is odd punctuation.
in the midst of a clutter of hands working for a single purpose, I found my home.
I really like this
When I walked into my first EMT class I quickly
EMT class, I quickly...
patients' life sagas
saga is an interesting choice, I'm not sure it has quite the right connotation
listening to my patients' life sagas when they want to be transported to the furthest hospital possible on a Sunday night and an ambulance bench that I spent countless nights sleeping on voyaging back to the station
This is a confusing sentence. It doesn't have parallel structure. I'm not sure which two ideas you are "between"
Despite the opinions of most who could not even fathom working under the stress and time constrains we are often put under, I think quite the opposite.
I might reword this. You think the opposite of what? You
can fathom working under stress?
I aim to never fail at my profession.
I like what you are trying to imply from the quote. I think it could be powerful (because you mean to say that you aim to never stop seeking knowledge and experience), however the message gets a little lost. When you read "I hope to never fail at my profession" it has a less-than good connotation to the reader. Maybe rephrase your last sentence
I really like what you are writing about. It is unique enough to catch the reader's eye and you talk about it passionately enough to keep them reading.