Kazza, I know you are exhausted but I agree with Lyn. Neither you nor your mum would be safe if she is discharged with no proper assessment or treatment.
I really think you need to put your foot down. It's not a question of you refusing to look after your mum, it's a case of keeping her (and you) safe. I suggest you tell the hospital that you feel she needs a specialist mental health / dementia assessment. She is ill and she needs treatment. And you cannot go on as you have been....
We are here at your elbow, willing you on, offering you virtual hugs and supportive cups of coffee / chocolate / bowl of pasta / whatever would help. Try to be clear with the hospital, then try to get some rest.
Take care
Lindy xx