Siblings are not facing reality. My siblings still expect me to do everything for Mom, even though I was recently diagnosed with congestive heart failure. I was forced to ignore my own health for 18 months, having to cancel one appointment after another, but I cannot ignore my health any longer. I am exhausted. My mom told me one day, "snap out of it!" My siblings feel I should continue taking care of Mom, as they "work."
I do not know which stage your mother is in or what her financial circumstances are, but it sounds like it may be best to see about assisted living for her. Since your siblings have not helped so far, they really don't have any dogs in the race, so should have no say-so. You decide what is best for your mother and you. If she is to the point of needing memory care in a NH, you may need to help her apply for Medicaid, depending on finances. I know it is a difficult thing to do, but we are as important as the person we care for. We have to tend to our own health needs and not theirs alone. Sometimes this requires help from a facility.
Let us know how it goes with you.
Do you have any help? I see that your mother has Alz. Are there enough financial resources so that she could go to memory care? Can you get some in home help for a period of time?
It sounds like an emergency sibling meeting needs to be called. And, "I am busy at work" is not an acceptable answer. In most American companies, you are allowed to take a sick day to deal with your parent's health. Be tough!
There's no way you can force others to do more, or convince them if they don't want to be convinced. All you can do is stand up for yourself and take time to take care of yourself. You have to learn to say "No, I can't do that." and "I'm taking the next two days/week/two weeks/month off to see my own doctors and after that I'll be following their recommendations in terms of rest, activity and follow-up. So you all are going to have to work out other arrangements for Mom." Say it and mean it. And stick to it. Seriously. If you collapse your Mom will be a lot worse off than she is now.