My mother is in a nursing home and the home is trying to make me pay her bills though I am not POA. Am I responcible for her debt?

Is there a POA? If so, tell the POA about the bills and give the home the POA'S information. The POA should be paying the bills with your mom's money in her account. Are you a joint/co-owner listed on her accounts? If so, then you have the ability to pay the bill by withdrawing the money from her account.