The first thing you need to do is be honest with yourself. You betrayed the person you committed yourself to until death and now you want everything to be normal. But it isn't. I don't know how possible it would be for you to have your marriage annulled. You would then have to be married in the Church, which could be done privately. You need to see your priest. But even if you are able to get an annulment, to begin a marriage as the result of being unfaithful to someone else, is a pretty shaky way to begin a new life.
You are definitely in my prayers--as is the spouse you left.
Fr. Vincent Serpa, O.P.