You asked two questions.
Were you at fault? What are your thoughts on that? Reading your post, it is hard to tell. If that is an actual,rather than rhetorical, question, that is a little concerning.
Honestly, the story as you explained it doesn't make sense. What kind of doctor ordered that? Let's put it this way- if the goal was hypoglycemia, there wouldn't be a better way to achieve it. The medication worked exactly as expected with a predictable outcome.
This was clearly a bad order. There were two opportunities to catch it. Either you or the co-signer could have prevented this.
Will you get fired? Ideally this will be an opportunity to look at a system that allowed three people to give the wrong medicine to a patient. The key issue may be education, or communication.
Ideally the patient did well, and you the doc, and the co-signer will all have had a learning experience that will reduce the likelihood of future errors, and the institution will change something.
There is no way to eliminate human errors. They can be reduced, and mitigated, but all humans make mistakes. I suspect that we all make errors that are never caught. For example, even had that patient not, somehow, become hypoglycemic, it still would have been a mistake to give the insulin. But, the mistake would have never been caught. And the process that allowed the mistake would have repeated itself, possibly with worse outcomes.
Look on the bright side. At least this
didn't happen. In this case, it truly took a village to harm the patient.