My father died without a Will.$55000 still owed on the house.my sister wants to buy me out of my share but but expects me to pay half the mortgage??

It sounds as though you know the answer.  Each of you inherits less the mortgage.  She pays you half of $94000 less $55000 and continues to make mortgage payments -- if the lender will accept her credit.  If not, she has six months after appointment as executor or administrator to sell the house before the lender has the right to foreclose.