CoffeeBlack,
Can you guys get her into hospice or home health care? Hospice will usually only take a patient if they are at "end of life", they provide comfort care to the patient which allows them to remain at home. It doesn't sound like your aunt is at this point yet but it may not be a bad idea to at least get a consult and maybe they can direct your family to some other services. At the least she will already be in the system when it is needed. In our area we have an organization called Senior Connection, they are very good at assessing a patients needs and providing assistance in obtaining services. See if you have something like that in your area.
I'm sorry you and your family are having to deal with all of this and my thoughts go out to you. Take care of yourself and keep us posted. Does allergy medication help with you cat allergy? I have a really bad reaction to cat's myself but if I take medication before going around them I can usually do ok for a couple of hours.
nj