It's certainly valuable to have some medical experience under your belt. It helps you to better relate to your patients, get accustomed to the operations of the hospital/nursing facilities and the jargon, plus it tests your ability to handle 'guts and gore'.
When do you apply to NS?
Volunteer work is a bonus. But your application will be impressive and tells a lot by your g.p.a., test scores, and often times they look at the dedication you have to whatever kind of work you do.
If you don't have any classes in the summer, see if you could volunteer a few hours then. Plus the kids should be out of school then. Also you could possibly find a volunteer site where you could take the kids along.