First thing is you need to stop being so hard on yourself. I don't really see exactly where you made a mistake. A lot of people were more knowledgeable about the patient and were continuing along a certain assessment/intervention path, which may have been the incorrect path in this case, maybe not. But I'm not seeing how this is your fault.
It sounds like you walked into this situation right in the middle of everything, and were not getting adequate feedback on the patient situation, and were trying to make some important decisions in a vacuum, and were also looking for some backup from other staff, and for whatever reason they were kind of slow on the uptake.
Sometimes a patient will decline very slowly and as much as it pains me to say this, sometimes staff does not recognize when the decline has gone from a concern to be monitored to something that needs to be acted upon immediately. It happens.
I have seen on occasion that a new person will walk into an ongoing situation like that with new eyes and see things differently, and it sounds like that is what happened to you. But it also sounds like the people who really knew that patient history were on a certain course, probably not the best one, and there was not a whole lot you could have done about that....it sounds like you were doing everything you could.
I have a feeling that this meeting is more about what was going on with the dr. and possible other nursing staff, and the facility wants to clarify the specifics of the situation for no other reason than to have clarity.
My suggestion is that you sit down and make a list, bulleted or numbered, of everything that happened from start to finish so that you have a clear idea of your role in the situation. Do not think about should haves, or would haves or blame or fault. Focus on the specifics only.
And for what it's worth, I don't think you should give up on nursing. You have some really good assessment skills, it's the action on those skills that will come with time. Give yourself that time and you'll do well.