No, Mary did not have the original sin. Christ saved her from it even before she was born, because the Savior was able to make a spotless tabernacle for Himself. This prearranged purity of Mary is evident in the words of the Archangel, “hail, full of grace”.
That Mary was human, the therefore had all the natural ingredients of humanity, including the ability to experience pain and death — is the Catholic teaching.
How do you go from "full of grace" to "no sin?" That is in no way evident.