I'm also surprised she wasn't sent home with a care-package. Clearly she's ill if she's on oxygen and suffering from heart-failure. This just doesn't seem right.
I think maybe you ought to be either talking to her doctor, or to your own - from your post it appears that the call from the doctor was made to her and, given how you've described her, she might well have given him / her the impression that she was coping on her own.
You may end up having to pay for carers to come in - or she will - but it's obvious you're not going to be able to cope otherwise.
I'd start by making a call to your own GP and let him know that you are literally unable to cope and ask him what you should do. If that fails - you can request to talk to her GP, he may not actually discuss her case with you, but he needs to know that his patient is, basically, in need of some form of care at home. Get the ball rolling, at least that way you can start to plan a course of action. If your mother spoke to him it's quite possible she allowed him to think everything was fine and dandy - he needs to know that it's not, and that you have not been given any instructions regarding her oxygen management or care.
Social services will always try to fob you off, but if her doctor gets involved, they won't be able to do that so easily.
I sympathise with you. What a terrible state of affairs. Elderly people are simply being pitchforked out of hospital and left to get on with it because the NHS and the care system is totally overwhelmed and underfunded.
Make a decision to make that call - or those calls - at least you will feel more in control of the situation, don't just struggle on, you can't manage this on your own.
