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.
If your illicit relationship with that man led you to commit fornication, you should know that you committed a grave sin and a hideous immorality. Allaah The Exalted Says (what means): {And do not approach unlawful sexual intercourse. Indeed, it is ever an immorality and is evil as a way.} [Quran 17:32]
Allaah The Exalted also Says (what means): {The [unmarried] woman or [unmarried] man found guilty of sexual intercourse – lash each one of them with a hundred lashes, and do not be taken by pity for them in the religion of Allaah, if you should believe in Allaah and the Last Day.} [Quran 24:2] Due to the gravity of such a sin, the corporal punishment that is prescribed for that crime in Islam is stoning to death for the married adulterer who is proven to have committed it.
Therefore, you should repent to Allaah The Exalted of that sin. Allaah The Exalted Says (what means): {… Indeed, Allaah Loves those who are constantly repentant and Loves those who purify themselves.} [Quran 2:222]
The conditions of good repentance are the following:
1. To give up committing the sin,
2. To feel remorseful about committing it,
3. And to be resolved never to commit it again,
Whoever fulfills these three conditions sincerely for the Sake of Allaah The Exalted, He Will Accept his repentance.
‘Ubaydah ibn ‘Abdullaah reported on the authority of his father that the Prophet, sallallaahu ‘alayhi wa sallam, said: "The one who repents from a sin is like the one who has no sin." [Ibn Maajah]
As for your question regarding swearing a false oath by the Quran (Mus-haf), you should have resorted to Tawriyah, (concealment of truth without telling a lie through using multi-connotative statements). You could have intended in your oath that he did not touch you in a lawful relationship or the like. It was reported on the authority of ‘Umar that he said, "Indirect speech accords great scope in avoiding lies." [Al-Bukhari in Al-Adab Al-Mufrad] [Al-Albaani: a Mawqoof Hadeeth and its chain of narrators is Saheeh]
Since this happened in the past and you swore a false oath to protect your honor and reputation, then this is considered a valid legitimate purpose (under the Islamic Sharee‘ah) and we hope that you bear no sin for doing so. However, you should turn to Allaah The Exalted in repentance and do more acts of obedience since good deeds wipe away sins.
Allaah Knows best.