Cool that you get to shadow! I would not list that on your resume necessarily, but it would be good to include anecdotes in essays, interviews, etc. I always think of resumes as listing experiences that you actually DID or participated in, while shadowing is mostly observation.
I volunteered at a hospital in MD. I was only allowed to do 4 hours per week (it was summer, they had school kids trying to earn volunteer hours, etc.), and I worked in ED Admitting. I didn't find it particularly enlightening; most of what I did was paperwork and, "Can I get you a blanket/ice/etc.?" Not to discount comfort measures, but it didn't give me a whole lot of insight into nursing.
If you are able, I would look into becoming a CNA or PCT and get a part-time job doing that somewhere. That has opened my eyes to the kinds of things working nurses encounter every day and has prepared me a lot better for what I anticipate in nursing school
. I'm sure the world gets a lot bigger as you start learning the role even more, but CNA by far was the best route for me.