I do not wish to sound uncaring, but I have to say that this is life, and as for you feeling disappontment and tiredness, you remember all the things your Mum did for you in life and get on with it. Explain to your work what has happened, there are very few companies that won't be able to put a plan in place for you until things are sorted, but seriously, you saying 'I never want another Christmas like this' and how gutted you are about wanting time off work, my daughter in law was doing all you are doing from the age of 13.
Her mum suffered severe depression, also had arthritis, could barely walk, and was incoherent in speech, and my DIL was left alone to look after her mum. Barely going to school, barely feeding herself, 7 years she did this alone until age 21 she finally got the help she needed to have her own life. She had to beg for every minute she needed from work, but she did it, because, to quote her 'Who else would care for her with as much as love than a daughter!'
Luckily the lady in question is a lot better these days, and feels terrible for the burden she put upon her young shoulders, but this is what family does. I know its hard, heartbreaking even. I have done this for my parents and step-parents, and it never gets easier. But you shoulder with a smile because one day, it will be us who needs people.
God bless and I truly hope you get everything sorted asap. xxx