With those hours there's no reason you couldn't get work in nursing/aged care- I'm a nurse and in the past have had availability of 4 shifts a week- and guess what- got all 4.
I'd be looking for something I can afford on my own.
Do you think you are blacklisted? I would be calling the previous agency asking what your status is just so you know.
Did you get black listed for breaking your lease? Like you didn't pay the rent out or lost your bond? If so then it would be hard to get a lease perhaps look for a private rental. If you not then you shouldn't have a problem.
I think you should apply for a job, tomorrow, if there are places nearby where you can work. You could work every Wed/Thur/Fri.
I also think you should apply for rentals, tomorrow. And lots of them, to increase your chances. If you can't afford a unit/house, what about a granny flat?
You won't get knocked back just because you've broken a lease previously, things happen. As long as you took care of your share of the responsibilities that will show.
You would be able to apply for a rental bond. I don't believe there is a limit to how many you've had, as long as you paid back previous ones.
I'm surprised that your mum is getting rejected due to rent arrears from 4+ years ago. As long as she has been up to date for a while it should be ok, it's always good to ask why you weren't approved for a place.
Go to EVERY real estate agency tomorrow. Explain what your looking for, the fact you need somewhere pretty soon. Also look into private rentals. A granny flat may suit you (and your budget)
Is it possible to look for places with your mum?
Most of all, good luck
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