GO SPEAK TO YOUR GUIDANCE COUNSELOR. If it were me, I would dump the pre-calc ASAP. Flunk it and it WILL pull down your GPA, and that's going to look the pits on your college applications. There are always alternatives, your guidance counselor should be able to help you out here.
What you have to look at is the university/college entrance requirements to both general admissions and nursing programs
. Pop into your school library "career" section, look at different schools
catalogs and decide on 3-4 that you'd be interested in attending. Then look at the requirements and plan your courses to match them.
As to whether or not it is necessary for 4 years of math "in order to be a nurse", I doubt it. A good grounding in basic math, ie algebra, fractions, etc is more usable than Trig. Someone out there might say differently, but I use a lot of basic algebra in my job.
Do I sound like a mom? Been there, seen it, done it with 2 great kids of my own. Good luck.