Refinance Advice

Cousin used the 150k equity in his home to buy an investment property with me late 2024. House was $566k, no other deposit just the equity so loan included stamp duty and fees etc was apx 600k. Remaining loan is 450k in both names and the house is owned tenants in common 60/40. I pay the total mortgage and all bills, he has paid for some upgrades, (windows, trees removed, security screens) and i am tenant (technically) in the house.

Cousin has sold house the equity loan came from and that loan is paid. And brought a new property. He wants me to refinance into my name only. I am a single parent with 2 kids earning 100k.

How do I refinance? Can I refinance? Should I in this current market? Do I need to do it sooner rather than later? Australia