Praise be to Allah.
There is no such thing as a so-called “white marriage”. Rather when there has been the proposal and acceptance, then the marriage is real, even if one or both parties to the marriage contract was only joking or playing about. This is the view of the Hanafis and Hanbalis, and it is the correct view according to the Maalikis, and the more correct view according to the Shaafa’is.
(See Fath al-Qadeer, 3/199; al-Mughni, 7/61; Kashshaaf al-Qinaa’, 5/40; Haashiyat al-Dasooqi, 2/221; Bulghat al-Saalik, 2/350; Nahaayat al-Muhtaaj, 6/209; Rawdat al-Taalibeen, 8/54).
The evidence they quote for that is the words of the Prophet (peace and blessings of Allaah be upon him): “There are three things which if done in earnest they are valid and if done in jest they are also valid: marriage (nikaah), divorce (talaaq) and taking back one's wife (after a first or second talaaq).”
(Narrated by Abu Dawood, 2194; al-Tirmidhi, 11849; Ibn Maajah, 2039, from the hadeeth of Abu Hurayrah (may Allaah be pleased with him). Classed as hasan by al-Haafiz ibn Hajar in al-Talkhees al-Habeer, 3/424, and by al-Albaani in Saheeh Sunan al-Tirmidhi, 944).
Jest refers to when what is meant by the words is something other than what is assumed. This applies to what you have done, because you made the marriage contract even though you had no intention of being married.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: “A divorce that is pronounced in jest takes effect according to the majority of scholars. By the same token, a marriage done in jest is also valid, as is stated in the text of the marfoo’ hadeeth. This is what was narrated from the Sahaabah and Taabi’een, and it is also the view of the majority of scholars.”
Al-Fataawa al-Fiqhiyyah al-Kubra, 6/63.
Ibn al-Qayyim said:
“In a mursal hadeeth narrated by al-Hasan from the Prophet (peace and blessings of Allaah be upon him) (it says): ‘Whoever does a marriage contract in jest or divorces in jest or frees a slave in jest, that is valid.’”
‘Umar ibn al-Khattaab (may Allaah be pleased with him) said: “There are four things which are valid if they are spoken: divorce, freeing a slave, marriage and vows.”
Ameer al-Mu’mineen ‘Ali (may Allaah be pleased with him) said: “There are three things in which there should be no joking: divorce, freeing slaves and marriage.”
Abu’l-Darda’ said: “There are three things in which joking is like speaking seriously: divorce, freeing slaves and marriage.”
Ibn Mas’ood said: “With regard to marriage, speaking seriously and joking are the same.”
From I’laam al-Muwaqqi’een, 3/100
Based on this, you do not have to renew the marriage contract; your first contract remains valid.
And Allaah knows best.