All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
What you and the lady to whom you were engaged did is wrong. Actually, you should not have done the marriage contract without the consent of the Wali (guardian) of this woman. Know that a marriage without Wali is a void marriage. If there were no witnesses, the matter gets worse. The Prophet said: “No marriage should take place without the consent (and presence) of a Wali and two witnesses.” [Al-Bayhaqi and Al-Albaani classified it as authentic].
Based on the above, this woman is still a non-Mahram woman to you. So, any intimate relations you had during this period is forgiven because of your belief that the marriage was valid in this way. But if you believe that it was an invalid marriage and yet you continued having intimate relations with her, then what you did was pure Zina (fornication or adultery).
In both cases, you should repent to Allah; first by giving up this illegal marriage, having remorse for this misdeed, and never doing this sin again.
After repenting, you should redo the contract in a correct way if you desire to live together with this woman according to the Sharee’ah.
Know also, that a Muslim should not do anything unless he knows its ruling in the Sharee’ah. Allah Says (what means): {So ask the people of the message if you do not know.} [Quran 16: 43]
Allah knows best.