It is not essential for you to be present at the marriage contract; what matters is that it be proven that you give your consent, and written permission is sufficient for that.
What matters is that your wali (guardian) or his wakeel (representative) should be present, because a marriage contract without the wali of the woman is not valid, because the Prophet (blessings and peace of Allaah be upon him) said: “There is no marriage without a wali.” Narrated by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Maajah (1881) from the hadeeth of Abu Moosa al-Ash’ari; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
And the Prophet (blessings and peace of Allaah be upon him) said: “Any woman who gets married without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid.” Narrated by Ahmad (24417), Abu Dawood (2083) and al-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami’, no. 2709.
From your saying “my parents do approve of this marriage but are not aware we actually had nikah” it may be understood that your wali was not present at the nikaah and that his representative was not present either. If that is the case then the marriage contract is not valid, and you have to repeat the marriage contract in the presence of the wali and two witnesses.
This applies if you have a Muslim wali, such as a father, brother or other guardian. If there is no Muslim wali then your wali is the Muslim qaadi (judge). If there is no qaadi, then it is the director of the Islamic centre or the imam of the mosque.
You do not mention anything about your parents’ religion.
Based on that, if none of your guardians are Muslim, then the way in which the marriage contract was done is valid. But if one of your guardians is Muslim, then the marriage contract must be repeated in his presence, or he must appoint someone to do the marriage contract on his behalf.
And Allaah knows best.