I agree with Vent. Get some other kind of cert that will get you hired in the hospital. You should definitely start working towards your BSN as soon as possible, but nursing programs are extremely competitive and usually perfect grades aren't enough. Most of the ones I've looked in to want prior experience. Unless your area is drastically different than mine, EMT-Is are not much more hire-able than EMT-Bs, and you'll be better off with a CNA and/or phleb, an MA cert, or something of the sort. There is so much that a CNA/tech/other lowly hospital pt care provider does that you do not learn in EMT school. I say this as someone who got my EMT in HS and is working through college (BSN pre-reqs) at a PACU as a patient care tech among other locations. Keep in mind though, I got really lucky and it is uncommon for someone with an EMT or even EMT-I to work in this sort of position, I've never seen it. Even most of the ER techs around here are EMTs and CNAs or nursing students.
You do not learn how to assist ADLs, work with foleys, or make a bed in EMT school and this stuff is the bread and butter of low-level hospital work and the fundamentals of nursing care in general. This is why I'm currently finishing up my CNA. I have heard lots of BSN preceptors and clinical instructors complain that their BSN students are coming to them better educated than years past, but less able to perform basic tasks such as the ones I mentioned above.
There are indeed some awesome scholarship programs at hospitals for nursing. Usually, they will pay for all or most of nursing school if you sign a contract to work for them as an RN for 2+ years.