The only advantage to having your EMT is that you may be able to get a job while you are getting your pre-requisites, and experience looks good when applying to nursing school.
HOWEVER... experience is much lower on the list of priorities for admissions boards than good grades. Focus on completing your pre-requisites and getting excellent grades in them. Learning another language, like Spanish, can also be very helpful.
I'd also encourage you to get your CNA instead of your EMT. You'll use more of the CNA skills in nursing school and as a nurse, and you'll be more likely to find a job in a hospital. Working in a hospital is more relevant to nursing, and many hospitals offer tuition assistance or reimbursement for nursing school.
This advice is from a CNA/EMT who recently finished all of her pre-reqs but didn't get accepted to her nursing school of choice because her GPA wasn't high enough (their stated minimum is 3.5, which I exceeded, but it's so competitive they haven't accepted anyone with anything below a 3.95 for years).