When I first started working as a ward clerk on my hospital's busy med/surg floor a few years ago, I had the pleasure of being trained by a very competent coworker who taught me a couple of very simple, yet effective things:
1.) "If you don't know the answer, FIND IT." All of our hospitals calls went straight to one of two ward clerk desks on our unit (and most of the time, we only had one working). All KINDS of questions were asked. She told me my job was to give people answers and make things happen. My question to her was "If you don't know the answer, what do you do?" She said, "If you don't know the answer, find it." This one baffled me for a long time, until I realized I would rather call lab (or x-ray, or CT, or dietary, or the nurse, or the doc etc) a million times to politely and patiently make sure I was entering orders correctly rather than guess without confidence; at the least delaying treatment and at the worst, injuring or even killing them.
2.) "There are almost no mistakes you make that cannot be fixed." Just knowing that most of what I did, although very different from nursing, was reversible (even if it wasn't easy) let some pressure off. Hand in hand with this information, she also taught me the same things your post discusses. If you make a mistake: recognize it, acknowledge it, and immediately find a way to rectify the situation. I have tried to do this in all of my work (as a med/surg floor CNA, a med/surg floor ward clerk, an ER mental health tech, an ER tech, and an ER ward clerk) ever since.
I am very grateful for her (and your!!) advice, and I hope to always keep these main ideas in mind as I will hopefully soon be starting a nursing program and most likely making lots of new mistakes!