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.
Marriage is one of the rituals that should be respected and honored by a Muslim. Allah says (what means): {And of His signs is that He created for you from yourselves mates that you may find tranquility in them; and He placed between you affection and mercy. Indeed in that are signs for a people who give thought.} [Quran 30:21] Also, Allah called it a solemn covenant; Allah says (what means): {And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?} [Quran 4:21]
It is for this reason that the Sharia set certain conditions for it, which we have already mentioned in fatwa 83629, so please refer to it.
Therefore, marriage must be conducted with the permission of the guardian and the presence of (two) witnesses, and they must hear the proposal and acceptance from both parties. As for what happened between you, a phone call and presenting the matter of marriage to you and you agreeing to it, then this is not a marriage to start with, let alone it being a valid marriage. Rather, what happened was just a kind of frivolous play.
Therefore, you did not become your cousin's wife by what happened. You may proceed with getting married, and you are not obliged to inform anyone of what had happened, including your parents and your fiancé.
We should also point out that if the marriage is one about which the scholars differed in opinion regarding its invalidity, then some scholars believe that there is no need for annulment or divorce, and some of them are of the view that separation should take place either by annulment or divorce, and that is the view that we adopt here at Islamweb.
Allah knows best.