OK - first of all, if you received a pay check from this employer, it will show up on your background check so you need to list it - or risk being accused of falsifying your information. The most important issue here is whether that employer has classified you as "not eligible for rehire" which is a red flag for future employers.
As an educator, I am concerned by the OPs overall tone of 'victim' - seems to be very little ownership of the issues. This will also be a major turnoff to any future hiring managers. Even though OP was given 'bad advice' on what to do, the ultimate result was a result of her choice. No one is perfect and we all make mistakes, especially when we're new or doing something for the first time. But the key is to take ownership and learn
from mistakes. OP needs to be able to articulate (when questioned in future job interviews
) what happened and what was learned. If she can do this in a way that is perceived to be sincere by the interviewer, it could really help.
From a patient safety perspective.. the behavior that was described by the OP is a classic case of "drift". So many staff are taking shortcuts (not documenting BP) that this has become the 'new normal'. But this is never a good enough excuse to violate acceptable standards of practice. It will eventually come back around and bit you right in the tush.