I think you should try and get the doctor to see her and let them decide what needs to be done.
Did the hospital discharge team not arrange for any external carers to come in to help? That's what happened to my 82 yr old FiL last year after he was admitted to hospital because he lost the use of his left leg. He was not discharged until a follow up care plan was made by the hospital discharge team. It was that team that ordered the equipment he would need at home and also arranged for a home visit from a care company on the day of discharge. He was discharged from hospital in the morning and the appointment with the care company was in the afternoon. The first carer arrived that evening.
Initially the care was paid for by the community NHS team because it was classed as part of his treatment. In other words his treatment was carrying on at home under the community NHS team, freeing up his hospital bed. This team only deals with discharged hospital patients.
Then, when he had recovered to a certain extent, he was discharged by the community NHS team and handed over to the Social Services team for an assessment of his care needs going forward. At this point he was waiting to see a consultant and unlikely to improve much more before then. In other words, that part of his treatment was over.
A social worker then visited him at home and arranged care for him until a financial assessment could be made by social services. In actual fact, all that happened was a change to who was paying for the care - social services took over payment from the NHS. The care carried on as normal.
Someone from social services then visited him at home and confirmed that he was not eligible for free care from social services because his savings were too high. So after the financial assessment we (me) had to arrange for a carer to come and the care would be paid for by FiL. The social worker gave me a list of the care companies in the area as my starting point and I spent a lot of time reading the Care Quality Commission (CQC) inspection reports until I had about 3 or 4 companies to contact.
I arranged for the new care company to visit my FiL to do an assessment of his care needs and then a date was agreed when the carer paid for by social services would stop and the new carer paid for by my FiL would start.
My FiL was and is far more able than your DM. When he was discharged from hospital he was able to walk with the aid of a wheeled walker and a zimmer frame. His problem was he could not get his socks and shoes on and off. He could manage everything else, albeit more slowly than usual. In time he came to only need help to get his shoes on in the morning.
Most of the care companies I contacted offered a minimum of one hour and we did not need an hour. Eventually it was the Social Worker who found us a care company that would come for 30 minutes. The only tasks the carer does every morning is put cream on his feet and lower legs (FiL is diabetic and needs to make sure his skin is kept in good condition) and puts on his shoes. The rest of the 30 minutes is filled with little tasks like light house work. It's almost a year now since this all started and 99% of the time it works well. But it was a lot to keep track of at the start and I was on the phone a lot. My FiL is hard of hearing and fiercely independent, so I was part of everything that happened (with the full support of FiL).
I write all this to give you some ideas of what should perhaps be happening with your DM. I don't have great health myself and it was a little while before my DH and I realised we were now caring for FiL, just not in our home.
Please ask for help because you need to look after your own health so you can continue to support your DM as time goes by. It's very tempting to say you can do something, when in fact you need to find a balance that works for you and your family. Just because you can do something doesn't mean you should be doing it. Best of luck.
and [hugs] to you all, you poor things. Really hope everyone recovers soon.