You have a couple options. First, you can pay for school on your own dime and hope that loan repayment is still an option when you graduate (it's 40K for the Air Force right now; other branches may or may not have it). Second, you could also look at ROTC scholarships
; only 2 years of ROTC is required to commission. Third, you could enlist as an ~E3 or E4 (google military pay charts) medical technician/corpsman for a couple years and apply for an enlisted-commissioning program (it's NECP in the Air Force, but all 3 branches have something similar); this way takes the longest, since you have to serve at least 2 years before you can even apply (average applicant has 5-8 years of time served).
Either way, it would be worth it to seek out healthcare recruiters in all 3 branches and weigh your options. Honestly, nursing is pretty much the same in all 3 branches. You likely won't get a response from a recruiter until next week at the earliest. A lot of people are gone during the holidays. Make sure you are talking to a healthcare recruiter; this is different from your average strip-mall recruiter (unless of course you want option 3). Healthcare recruiters only recruit doctors, nurses, pharmacists, etc to commission (not enlist) as officers.