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.
First of all, we pray to Allah Almighty to make you and us steadfast on His Religion till we meet Him. You have to be grateful to Allah for guiding you to Islam, which is the greatest bliss that Allah has ever bestowed upon you. As to your marriage from that man without the presence of your Wali (guardian) and witnesses, it is invalid.
For more benefit on a woman’s marriage without guardian, please refer to Fataawa 92758, 85057, 226429, 132754, 81777 and 269080.
If you are willing to continue in your marital relationship, then you have to renew the marriage contract while fulfilling the conditions and prerequisites of a valid marriage, such as the presence of the Wali and witnesses. But if you want to discontinue this marriage then there is no need for divorce because you are not legally married. The sexual intercourse that you had with your husband during the past period is not considered fornication; rather, it is a doubtful marriage. Children in this case are to be traced back to their father, but you have to be divorced immediately for if you have sex after you have known the ruling, then you will be committing fornication. If you wish to remarry this man, then you do not have to observe an 'Iddah (waiting period). But if you want to get married to someone else, then, in this case, you have to observe an ‘Iddah for three successive menstruation periods.
Ibn Qudaamah said in Al-Mughni: “A woman who was married a doubtful marriage should observe the same ‘Iddah as that of a divorced woman. The same thing is applicable to the woman whose marriage is invalid. This was the opinion of Ash-Shaafi'i because having intercourse with a woman in a doubtful marriage and an invalid marriage in relation to engaging the womb and the rights of lineage are similar as a valid marriage. So, the procedures followed in relation to attaining certainty (by having ‘Iddah) are the same.” [End of quote]
He also said:
“A woman who is in the state of ‘Iddah after an illegal marriage such as fornication, or having had intercourse in a doubtful marriage or invalid marriage, then the analogy drawn by our School is that her marriage is unlawful whether to the man who had sexual intercourse with her or someone else. It is more appropriate to consider her marriage lawful if it is with the same husband from whom she is staying in Iddah if her child is traced back to his lineage. This is so, because the reason behind ‘Iddah is to preserve his water (i.e. sperm from being mixed with other sperms) as well as the lineage. And there is no importance to preserve the husband's illegal and legal sperm from getting intermixed and this has no influence on the lineage.” [End of quote]
For more benefit on a doubtful marriage and observing ‘Iddah from such a marriage, please refer to Fataawa 124014, 233893 and 275158.
Allah knows best.