pls help, no recourse to public funds and being evicted

[ultrasound]

Hi all, just joined this forum.
I got my BRP (work permitted with NRTPF) a day after my friend i was living with ASKED ME TO LEAVE her house. i got to live with this friend when i fled my husbands place due to series of Domestic violence issues in the presence of our daughter.
When my BRP came, i went to social services no recourse to public funds in the bourough i thought i was under, long story short, they referred me to my appropriate borough and sent all my documentations to them by fax.
i went in to see the staff as they requested i come in, was harassed verbally by the first social worker who said they would foster my child if i cant provide accommodation for her, i should give her to the dad as he has parental responsibility, or send my child back to nigeria while i sort myself in the uk. after interviewing my daughter and i, they came back with a twisted version of our account, most of which we did not say, in the end, they gave me two options, (1) to support me in voluntary repatriation to nigeria, should i wish
(2) if i refuse this offer then the local authority can offer section 20 accomodation for my daughter until i am able to resume care for her.

i went to these people to ask for a short term help due to this sudden eviction, i did stress i am not after any sort of benefit as i am a UK qualified maths and science teacher looking for work as soon as i got my BRP. but unfortunately, my friend who was helping us needs her room to put an au pair.
my childs school tried to use school and church funds to help, but the social services said they would be breaking the law of no recourse to public funds.

Who and where do i go to for help now as i am due to start agency work as soon as my DBS clears. any advice would be appreciated, thANKS