That does sound like an option lurching, not sure how it works in engalnd but you certainly can check yourself into a psychiatric hospital, or at least turn up and ask for an emergency assessment at which point they will decide (assuming they have space for you) to take you in for a while to find out if you are safer at the hospital. If not, they will at least have advisors on hand who can tell you exactly the best way to manage if they turn you away and hook you up with the correct support you need, be it medications or personal help. They will be VERY sympathetic with you.
I'd say give this a shot FG, if you can, as the council know jack shit about this sort of thing and are more concerned with practicalities and beaurocracy. These hospitals have all sorts of specialists and therapists on-site used to helping people through the kind of issues you have or are facing.
Particularly the way you've been talking, if you are feeling or have been feeling atall suicidal then I would advise you to look into these options I've outlined.
p.s speaking from my own experience, having spent a few stays in psych hospitals myself, they are nothing to be afraid of and are incredibly supportive.