First of all: the priest is bound to absolute secrecy. Now, depending on what you confess, there may be a reparation to be done in order to be absolved, and it may be up to you whether or not you are willing to do it. But that is only speculation until you actually confess. It is, however, a sacrilege to be aware of mortal sins and not confess them, and a greater sacrilege to receive the Holy Eucharist in such a state.
That being said, it seems to me that your statement about a sin "too great and disgusting to admit" reveals truly a great candor in your heart, though perhaps you yourself are unaware of it. Perhaps you have not learned that in Confession the priest acts in persona Christi, meaning you confess to our Lord Himself, and it is the Lord Himself who absolves you - the priest being "merely" His chosen minister. And the Lord God "sees what is done in secret" and willed that "there is nothing secret that shall not be revealed", thus you are truly not telling Him anything new. Do not let yourself be stopped short by the intermediary, that is, the priest...you are talking to Jesus Christ, who has witnessed the greatest abominations, and who took on Himself the greatest sins, namely the most grievous offenses done to His body throughout the Passion, culminating with the piercing of His heart after His death.
I do not think that at this point you have read anything on the Spiritual Exercises of St. Ignatius of Loyola. That superb spiritual warrior and founder of the Society of Jesus described fairly well how Satan works with regards to confession:
Likewise, he acts as a licentious lover in wanting to be secret and not revealed. in the same way, when the enemy of human nature brings his wiles and persuasions to the just soul, he wants and desires that they be received and kept in secret; but when one reveals them to his good Confessor or to another spiritual person that knows his deceits and evil ends, it is very grievous to him, because he gathers, from his manifest deceits being discovered, that he will not be able to succeed with his wickedness begun.
Ultimately there are two masters: Christ, Lord by God's will, and Satan, master by usurpation. When we sin, Satan ties a mystical chain around us. There is only one way that we know of to break that chain: the Sacrament of Reconciliation, in which Christ Himself breaks the chain and restores you not just to forgiveness, but as if you had just been baptized - you would be pristine and pure. This is what the Holy Spirit spoke through the prophet Isaiah:
I am, I am he that blot out your iniquities for my own sake, and I will not remember your sins.
Humble yourself before Christ and confess openly everything, knowing that the priest is under the sacramental seal:
every priest who hears confessions is bound under very severe penalties to keep absolute secrecy regarding the sins that his penitents have confessed to him. He can make no use of knowledge that confession gives him about penitents' lives. This secret, which admits of no exceptions, is called the "sacramental seal," because what the penitent has made known to the priest remains "sealed" by the sacrament.
The secret of the sacrament of reconciliation is sacred, and cannot be violated under any pretext. "The sacramental seal is inviolable; therefore, it is a crime for a confessor in any way to betray a penitent by word or in any other manner or for any reason.
"A priest, therefore, cannot break the seal to save his own life, to protect his good name, to refute a false accusation, to save the life of another, to aid the course of justice (like reporting a crime), or to avert a public calamity. He cannot be compelled by law to disclose a person's confession or be bound by any oath he takes, e.g. as a witness in a court trial." (source)
I will finish with a last recommendation: the best and most direct way to not only achieve self-mastery but to eradicate lust from your soul is to develop a strong devotion to the Blessed Virgin. The more you love her, the greater purity you will receive in your soul. She herself will plead to God for your sake, and it has never been heard that a prayer of the Virgo Prudentissima has not been heard and granted by Christ, Her divine son. I recommend the reading of "Treatise on the True Devotion" by St. Louis-Marie Grignon de Montfort, as well as "The Imitation of Mary" by Thomas Kempis (yes, there is such a book, for those who only knew about "The Imitation of Christ").
You have not yet tasted freedom. Once you do, you will never again willfully become a slave of lust. You may fall under its weight, but as one warrior wounded by another, not as a slave following a master in chains.
Welcome into Holy Church, brother. Rejoice and be glad, for the Lord said: "Nobody can come to me unless the Father draws him. Many are called, but few are chosen."