HMCpl

I've seen NJPs for sunburns. It's up to the command and how they choose to persue it. Improper use of government equipment fits. Even malingering is a violation of the UCMJ. Getting busted down for any myriad of offenses by NJP is not at all uncommon in the enlisted ranks. Now, I'd be worried if the OP were talking about a Court Marshal. That is serious.

I wouldn't worry about it. I currently work with a BSN who was prior Army who also got a reduction in rank. The only reason I know about this is because he told me while we were talking about service. On all the applications I've ever filled out, the only thing they actually care for is the condition of discharge. What you choose to disclose after that is up to you. From what I've seen, the only time people really care much about your condition of discharge is in the government sector. If you have an honorable discharge (and you have a good reenlistment code) then you aren't likely have problems getting a government job either. Speed-bumps in your military career matter far less than its final condition. You're good.

You might have an easier time going Navy. You might find an easier translation of your service. I'm not taking about related to your MOS necessarily. More like awards and time. The Navy also has a DCO program for medical personnel. Go reserve and you can get your military nurse experience while you work on going active.