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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, we congratulate you upon embracing Islam and we ask Allaah to make you firm and steadfast on this religion until the day you meet Him.
It is true that the presence and consent of the guardian [Wali] is a condition for the validity of marriage as the Prophet said: "Any woman who gets married without the consent of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid." [Abu Daawood] So, when a woman of the People of the Book marries, her guardian should be from her religion [either her father or his agent]. So if the matter is as you mentioned that you married without the consent of your guardian, then the marriage is void. However, if you have any children from this marriage, they will be traced back to their father because, when you married, both of you thought that the marriage was valid.
Now you can renew the marriage contract and have a Muslim guardian for the marriage since you are now a Muslim. However, if you have no Muslim guardian, you may take your case to an Islamic centre so the people there can marry you off.
However, if your husband married you without a guardian believing in the opinion of some scholars that marriage without a guardian is valid, then the marriage is correct [and you do not have to renew it].
Allaah knows best.