Hi Liz2034,
It is not clear what you mean by the decorator receiving half of your rental income.
I'd recommend you call the tax technicians at HMRC with some basic amounts of renatal income and expenses so we can consider whether you have any income from property first of all.
I am not able to answer your question about Carers Allowance but a call to HMRC may help you find out what is potentially a taxable income.
Income Tax: general enquiries
Thank you.