I felt exactly how you described when I first came off of orientation. I thought it was a unique feeling and I could not fathom that every nurse feels like this when they start. But the crazy thing is one day, after a year, I realized I didn't feel like that anymore and I saw other new grads coming in after me feeling the same way that you are feeling and the same way I felt. I also noticed many nurses gave me a hard time about small details when I was new and they eventually let up on me and started doing that to newer people. Whether it's because of the whole "nurses eat their young" idea or just that they're trying to help bring your attention to these details that you're overlooking. With experience and time, others around you will see your unlabeled tubing and trust that you are going to label it before you leave and I would honestly just throw a gown on before going in.
I can almost promise you that after a year or two you will be almost like your buddy - helping out other newer nurses with easier assignments. You will get the hang of it and get faster at doing the "tasks." From what it sounds like though, you had a lot going on at once and prioritized correctly. The next time you have a day like this, you will just move through everything quicker and it will all come together.
As far as your other patient *shrug* He will be fine. I once had a coworker's patient request to leave AMA when it took "20 minutes" for someone to put him on the bedpan. It was 10 minutes tops. My coworker said "OK" went straight to the filing cabinet, pulled out the form, called the supervisor and went into his room to let him know the process of leaving AMA. He ended up not going because he just wanted to whine but my point is, you will eventually realize when their complaints are valid and when they need a small reality check. While I get your reaction and I know you're only human, I would have apologized (we're in a service based profession so we're always apologizing for things out of our control) and informed him that there is another patient who is doing really bad. Almost every time, they say it's ok because it hits them that they're in a hospital and people could actually be dying. However, I've seen other nurses react as you did and you're not totally wrong - he has to wait.
I remember when I first started and I got a call from the lab that my patient's hemoglobin was like 5 and I had to do a transfusion and I panicked and was frantic and blood transfusions were the scariest thing. A few weeks ago I had 2 in one shift and was like meh. You will eventually get that way with time. In about a year you'll be dealing with a low BP like meh. I know it feels like a nurse, even a new one, should be confident and know it all but that's just not the reality of it.
Give yourself time and you will eventually become a great nurse.