All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Your marriage is null and void for the Hadeeth which you mentioned in the question that the Prophet said: “Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid.” [Abu Daawood, Ibn Maajah, Ahmad and Ad-Daarimi]
Moreover, the Prophet said: “There is no marriage except with (the consent of) a guardian.” [Ibn Hibbaan].
Therefore, you are both obliged to immediately separate from each other and then renew the marriage contract if you wish to marry with the presence and permission of your guardian [and the presence of two witnesses]
However, if you had sex with each other, it is not considered Zina (fornication or adultery); rather, it is a doubtful marriage (i.e. you married each other while believing that the marriage is valid). If you had any children from this marriage, they are traced back to their father since the Hanafi School of jurisprudence rules that a marriage without the guardian is valid but the latter has the right to cancel the marriage if the woman marries an unsuitable man.
Allaah Knows best.