I'm sorry to hear about your situation.
It's
probably not dire enough to warrant refugee status.
In hindsight everything seems more clear but I do wonder, if you got 6 months in NZ, why is it only now that you start trying? 6 months is a pretty short course, is there no way to extend/deepen your education and by doing that extend your visa?
When it comes to getting a job in NZ you've at least got the advantage of being in NZ. Many employers from NZ want face to face meetings and at the very least you have that choice.
Speak with INZ because in the end, their word is law. While I'm sure there is sympathy for you, I suspect that it's better to come with a pro-active attitude and ideas on your future rather than a sad story (even if it's a true story). It's possible your native tongue (Spanish?) would be a useful skill not TOO many people already have in NZ.
When it comes to staying
you need money/skills/job(offer)/sponsor/genuine fear for your life if you're sent back/a study/claim to (partial) NZ nationality/Experience if not schooling in an essential job with employee shortages.
^ You need at least 1 out of 8 to even begin the conversation. I would suggest you look how many (if any) you have and if you can change that in the time left.
I've given you advice based on my experience as a refugee services worker in my country which I believe to be good advice.
Immigration NZ (INZ) is the king in this domain though and if you can't find a way with them, there is no legal way to stay.
Sorry if I seem cold/detached. I do care, just trying to be practical.
Good luck with what comes next Vene!