Well first, realize that while going to a prep school increases your chances of getting an appointment; assuming you do your part; there is no "Guaranteed appointment".
Also; going to NMS and redshirting will keep your NCAA eligibility open, but again, that is not a "Guaranteed Appointment". If your athletics was guaranteed, then they would have given you an appointment this year (2015). Unless your grades weren't good enough, and therefor them offering you some sort of a prep school was their way of getting you in.
Now; if you turned down a prep-school or military college offer, then honestly, you turned down your best chance of receiving an appointment. Obviously it's too late to change your mind, but hopefully others reading this thread will realize. "If you are turned down to the academy; and you really truly want an academy appointment and to serve; and you're not just looking for a free education; and you are offered a PREP-SCHOOL or a Military College SLOT....... YOU TAKE IT!!!!!!!!!!!"
But you've already made your choice. So; go to New Mexico state and apply to the academies now. If you think your academics aren't very good, then maybe holding out on your NCAA eligibility will help. But only you can tell if you think you have a good chance of getting an appointment. If you don't think it's a great chance, then keep applying, and do track at NMS. You can't put off your life because of what MIGHT happen. Remember; there were approximately 12,713 initial applicants for 2015. Of those, 1,159 started BCT. That's 9.1%. If you want the academy bad enough, you'll use every edge you can. But only you can decide what to do next. No matter what option you took, you'd have to wait at least 1 year before the next class; so I don't know what NMMI would have been too long of a wait. It's the same wait as every place else.
But again; only you can decide. You already removed certain options and opportunities. Now you have to work with what you have left. Best of luck to you.