Quote from idkmybffjill
Programs aren't going to expect you to be able to draw blood to get admitted. That's something you'd learn while in the program, not something you need to know now. I'm not even sure if that's something that they'd care if you know or not.
Volunteering at a hospital may help more than volunteering at other places depending on the program. Some programs don't care while others may look more favorably upon volunteering at a hospital specifically. Honestly, the best thing you can do is talk to the nursing advising staff. Schedule an appointment with someone to make sure you are on track with everything and ask them what they feel would help you become more ready to apply to the nursing program. This way, you know specifically what your program looks for AND you can start getting familiar with the people running the nurse program (and they can get familiar with you). If they know your face and know you are putting effort into getting into their program, they're going to remember that when looking at applications.
Going off of this a bit... Some schools (like the one I'm at) only look at two things when you apply to nursing school- your GPA, and your TEAS exam; unfortunately (or fortunately, for some) they don't care if they know you or if you have relevant experience (as a CNA, MA, LPN, etc.)
Perhaps some important questions to ask would be what factors are the most important when trying to apply for a nursing program. I see a lot of people on here say that their programs look at their science grades. My program looks at your overall GPA, so good science grades are only relevant in helping you boost your score. Some schools are so competitive, you basically need all As to have a chance of getting in. At my school, the TEAS exam has the greatest impact on whether or not you'll get in.
It all depends on the school, so like "idkmybffjill" said, it's best to talk to an advisor at your school to see how you're shaping up and what your goals should be.