It's technically incorrect to say you inherited when the estate is insolvent. As an heir you have no obligation to file a petition for probate. If you do then you take on the duties of an administrator or executor and can be paid out of the assets of the estate a reasonable fee for administering the estate (before any claims that don't involve liens on real estate). The reasonable consts of administration of the estate are payable prior to any unsecured creditors. Additionally if there is a family exemption that gets paid before any creditors get paid. You should talk to a seasoned probate attorney about how to proceed whether or not you have already filed a petition for probate.
You indicated that you inherited a "mortgage" and "property tax" which leads me to believe that real estate also appears to be in the decedent's name alone (and please correct me if I am wrong).
Without knowing more facts, I would suggest that you consult with an attorney who practices in this area in order that a clearer picture can be painted.
Undertaking an estate is rather time consuming - it also carries with it the fiduciary duty to do things properly and by the book.
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The other attorneys offer good advice and you should have a consultation. Some estate like this are better to just walk away from.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.