Even if you are the one who helps admit your mother to the hospital, it is not likely that you will be legally responsible for covering her medical bills.
In general, you would be personal liable for your mother's debts only if:
- you agreed in advance to be personally responsible, such as by co-signing or guaranteeing a particular transaction
- you are liable for the debts because of another legal relationship that results in a duty of support, such as you claim your mother as a dependent, or
- your negligence caused the debt, which does not sound likely in this case.
While that is the ultimate legal reality, however, given the current state of the medical establishment and of the world in general, know that doctors and hospitals might attempt to collect from you after your mother's death. Just to be sure there are no ultimate mixups, it's a good idea to encourage your mother to keep good records of her medical bills and payments—or keep them for her if she agrees.