I haven't personally seen propofol raise the heart rate. I think more likely the hydralazine had more to do with it. But as in all ICU patients (Neuro, Trauma, Burn, MICU/SICU), a number of factors could cause any little set off. You have to look at the whole picture and then dig a little deeper sometimes.
LCCC is tough with their nursing program because they have so many applicants per year. They may keep you out of the program until you take all the prerequisites but they may provisionally accept you into the program pending the completion of your MA101 class.
I have used a Littman Cardiology III for some time. I had to send it back twice to have the tubing replaced because the oils from my neck wore down the tubing to the point of cracking. I still do not use a cover, but I rarely put it on my neck anymore. I just keep it in the cargo pocket of my scrubs. To each his own. If you want to use a cover, go right ahead. I'd be more embarrassed about having a Bears logo on it than the cover itself. LOL