Since you were in enlisted status at NAPS, and were presumably separated from military status, you probably have a form in your NAPS paperwork with a code on it that indicates whether you are recommended for further military service, either at all or completely or with reservations. It’s usually called an “RE code.” Start there to determine if you are eligible to start down a military commissioning path again. That will determine if you can be accepted into a NROTC program.
This is not an official source but is usually reliable:
RE codes, found on military discharge documents like the DD-214 define a service member's future eligibility to enlist or reenlist.
veteran.com
In addition to excelling in all the usual ways, you will have to believably demonstrate in word and action how you have changed and learned from your bad choices at NAPS. The Navy invested a big chunk of taxpayer money in you, and you bit the hand that fed you. Conduct issues are one thing, but honor brings along the twin of lack of trustworthiness. That is a large rock to overcome.
I will say that it did bother me that I didn’t see in your post how you have taken ownership of your choices, are truly remorseful for your honor offenses and have committed to better choices - but perhaps that is the challenge of reading a post in an anonymous forum without benefit of eye contact, body language and intonation.