My job is a little shady help me out?

Please ask your Human Resources Manager about vacation time policies

If they hired you with the intention of you only being there for about 1/3 of a year, giving you 1/3 of a year's vacation seems perfectly reasonable.  Letting you go at the end of that period, especially if you have nothing to do, would also be a reasonable move on their part.  Hopefully you have already started your search for your next job.  

There's other possibilities as to why other staff has more vacation time.
- they earned them because of how long they've worked there.
- maybe there's been a policy change and that's what the old PTO policy was and the people who have 3 weeks have that amount of vacation because they were grandfathered in, you were hired after the policy change and got the new amount of vacation.

It's not going to hurt to ask HR about it: "I heard other staff has 3 weeks PTO but I only have 5 days. Why is that?"

You've only been there for four months.  You don't qualify for three weeks vacation.

You claim you where hired FOR THE TRANSITION, and wonder if they may get rid of you now that the transition is over.
1 hour AFTER posting this question, you ask how long it takes a state to approve your license, but you seem confused about why your current job doesn't involve actual nursing.
I HOPE I never need medical care anywhere near you. If you are not a troll, your nursing license isn't worth more than my CPR certificate.