She was unprofessional, but you were even more so. Calling her a bitch? Really? This isn't junior high here.
I would learn to disengage from these situations and to not give people fuel for the fire. Unfortunately, if you go to HR, it will look exactly like what it is: a cat fight. And if they see it that way, you will either both be ignored, both be reprimanded or they will believe her because she was the RN on shift.
Haven't you had work issues before? If so, maybe it is time to take a step back and look at how your behavior and reactions may be fueling some of these issues.