Securing a new-grad position in CA is hard, no doubt. From the conversations I've had, they see something on the order of 100 applications for every new-grad posting.
+ being a veteran helps, particularly in a USN-centric town like SD. Our society presently lionizes veterans so that will certainly work to your advantage. Recognize, though, that formal 'veteran's preference' is not universal but rather a hospital-by-hospital policy.
+ being bilingual in Spanish is huge (a bit of Tagalog is meaningless unless "a bit" is "quite a bit")
+ a BSN is borderline mandatory for many new-grad positions in CA, especially at the big hospitals
+ Corpsman experience is very helpful because it means that you can show up to work every day and handle your stuff. Don't think it makes you 'all that,' though, because it's a whole different realm of the medical spectrum. I had an acquaintance tell me in admiring tones, "they can even do stitches..." which was meaningless because we don't suture... the MDs suture. In SD, you're more likely to run across managers who've come out of the Navy, or at least have Navy connections, and who will recognize your experience as more meaningful than will folks with no military connection.
My recommendation would be to cast your net far and wide and to take whatever job you can find (hint, look rural... very rural). After a couple of years, you become a viable candidate for postings that you have no shot at as a new grad.
How much trouble you'll have getting hired is hard to say but from the little that you've posted here, I'd say you're more competitive than many new grads.