Advice urgently needed re housing

Hi, firstly, thank you for such a supporter and informative site.
I don't know where to start, but here goes... It's very tricky putting this into words.
I'm in the process of leaving (divorcing) my husband on grounds of emotional abuse.
I'm in receipt of PIP enhanced rate of both, and also have been granted Universal Credit. At the moment I'm still in the marital home (his house) living separately from home.
I'll be having to leave here as soon as my financial settlement is through under £17 thousand. So will have enough for a private rental deposit. I suffer from acute anxiety and depression, amongst other things. So I will need to get away as soon as I can. I've no idea how the housing benefit scheme works. Is it up to the local authority near where I'm relocating to. I'm so sorry to ramble on, but am in tears as I write this as it all feels so overwhelming. My daughter is looking at a private rental property this afternoon. I must add, I have a smallish dog, my doctor has written a letter stating she is my emotional support dog. I just don't know where to begin to get started with who to contact and how much rental I could be helped with. This is very embarrassing for me. But thought if anyone could help advise me it would be you guys. Thank you for reading xxx