I am terribly sorry to hear that you are suffering right now, and I assure you that you have my prayer that you will be able to carry this cross of yours! I know that it can be incredibly difficult, but try and think not of it as a cross, but as a blessing. God wills and permits all things for our greater good as it is known to Him, and we know that He loves us unconditionally. Which means that no matter what we face in life, we face because in the end God will bring out a good for us from it.
The Catholic doctrine of "offering it up" may be a little hard for you to understand since you come from a Protestant tradition, so do not worry about anyone "having a pop" at you. Quite simply, when we are in a state of grace, by our actions we can merit for others (those suffering illness, spiritual temptations, the release of the Holy Souls in Purgatory, etc.). This can be accomplished because being in a state of grace means we possess habitual grace, which is the indwelling life of God within us. It is the participation in the divine nature of God. Catholic Answers has a tract on this subject and it adequately states of sanctifying grace (habitual grace): "Sanctifying grace stays in the soul. Its what makes the soul holy; it gives the soul supernatural life. More properly, it is supernatural life."
The meriting that can be done whilst in a state of grace is fully reliant upon God's grace. The value of our acts take their value from God Himself. He gives them worth. Hence when we are not in a state of grace, when we are in a state of sin and death, we cannot merit anything by our prayers and good works.
The best spiritual use of your illness would be to listen to God's call to you to receive the Catholic faith and come into the practise of the Catholic religion.
Your question on the particular issue of the doctrine of "offering it up" and your statement that you are, at least, "Catholic in heart" say to me that He is trying to draw you closer and closer to Him. We enter into a state of grace, we come into the possession of habitual grace, by Holy Baptism. But sadly by sin we lose that same grace. But wonderfully and joyfully Christ has instituted the Sacrament of Confession which is administered by His ministers in the Church every day, and by it we can be restored to our participation in the divine life. Furthermore you have implicitly acknowledged a desire to serve God and others through your trial, that your suffering may avail others as Christ's own did. This oblation of yourself seems a foreshadowing of the sublime oblation we make of ourselves in Holy Communion to Our and Saviour Jesus Christ. As He has came to us, as He has given himself entirely to us, He asks in return that we give ourselves entirely to Him, and this is no better accomplished than in the act of Holy Communion! I could go on and on. I don't think you can deny it, you have to swim the Tiber!
Yours in Jesus and Mary,
SCIM.
