Help with housing

[feathermum21]

Hi, I'm looking for some advice regarding housing benefit but first I'll give you some background...
I'm a single mum to my soon-to-be 5 year old who has complex special needs. We currently live with family (5 adults) in a three bedroom house and share a bedroom and bed. As I said 5yo has lots of complex needs and one of them is being tube fed through the night, neither of us have had much sleep in the last two years.
I've applied to the council countless times and they've said although they acknowledge our situation is far from ideal they don't count us as a priority, I'm at my wits end.
I work 16 hours a week and we currently get working tax credit, child tax credit, and DLA for 5yo. I'm looking at private renting but I was wondering is anyone could offer any advice on how much they would likely to cover for the rent?
And if we were to get a three bedroom would they not cover anything at all? The problem I'm having is finding a two bedroom in our area and the three bedrooms are mostly the same price as two beds, some even cheaper!!
I've tried doing the online calculator but I'm finding it so confusing. Thanks in advance for any help you can offer 

Check the LHA (local housing allowance) for your area. A quick Google should show you how much you would be entitled to for a 2 bedroom place. You would put that against the cost of a three bedroom place. Once you have a LHA figure go onto either entitled to or turn2us calculator if your local council don't have their own online calculator. It shouldn't take long to fill in and get an answer. Good luck.

You will be entitled to the lha for a two bed place. This ammount varies according to where you live so as pp says find that figure. Because you work you won't get the full ammount but can use it towards a 3 bed place if you can afford to making up the shortfall with wages and other benefits.

I live in surrey and they cover 880 per month if you qualify for maximum entitlement. Inner London is 1100 I think

Thanks so much for your help everyone, I've managed to find a lot more info, think I will continue in my search for a two bed