No, you are not liable just because she is your mother and just because you have a power of attorney. But that is not the only issue. Many hospitals, doctors and nursing homes demand that the person signing in the patient, the relative who signs the paperwork, also sign on documents saying that you will pay all the bills. This can get tricky and can be slipped by you if you are not watching for it.
It would make sense to check into this now, before her medical bills pile up. There may already be one of these agreements that you signed without knowing it. You need to protect yourself.
I suggest you call me. I will assist you. No charge for the first office visit.