If you don't already have your EMT-B you can get it in one semester, it's only like 100 hours or so, don't quote me. I went to Century college for my Paramedic it was 18 months and EC took many of my EMS credits I think 30 to be exact.
Being a Medic is the best job i will EVER have! I love it, I worked in Baton Rouge Louisiana . I saw just about everything you could see on the streets. But EMS is extremely hard on your body, a lot of heavy lifting.
I am sure you can get your paramedic cert and apply to EC but I would suggest getting some good experience under your belt before trying the Nursing thing.
I think the only reason this course is even possible for me is that I have 10 years of Hospital/ EMS experience...it's a lot to think about, so good luck. Hope I didn't toot my horn too much and actually helped you a little...