Legal Question in Credit and Debt Law in Pennsylvania

They are not trying to "damage your credit rating." That is not their aim. They want paid. As it appears that your mother is deceased, did she have a will? If so, did the will name you as executor of her estate? If there was no will, has anyone (either you or your brother) sought to probate her estate? If not, then you need to talk with the clerk of the probate court in the county in which your mother resided at the time of her death. If your mother lived in PA, this is called the Orphans' Court. It goes by other names in other states.

You need to find out from the clerk whether you need to even bother with probate of your mother's estate. If all she had were personal items and no real assets like a house or car or money in the bank, probate might not be necessary. If it is necessary, then the executor named in the will needs to apply to the court to get officially appointed. The executor will then have to contact the nursing home and direct them to file a proper claim with the estate.

If probate is not necessary, then the executor (if it would be you) should write to the nursing home, state that your mother has passed away (send a copy of the death certificate), and explain that there will be no probate as your mother has no assets in her estate.

If your brother signed something that makes him financially liable, that is between him and the nursing home and they can contact him for payment. If the nursing home still contacts you, they have no business contacting you and you need to dispute this in writing by telling them not to bother you if you are not the financially responsible party. You should not need a lawyer. If you signed absolutely nothing, then I have no idea why they are seeking to hold you responsible.