Jesus was not asking if his Father was willing to heal him because Jesus was not sick. Jesus was asking if there was some other way to redeem the world other than his suffering and death. The answer to that prayer was "no", but the Father graciously sent an angel to strengthen his Son in his time of anguish.
So the idea of "if it by thy will" (to heal) is not justified by Jesus' prayer before he died. We've looked at suffering on behalf of preaching the Gospel (which Jesus certainly did) in other posts. We will come back to it again soon when we consider Paul's "thorn in the flesh".
Let's look now at the idea of "offer it up" which is another popular response to illness. Offer it up seems to mean that we are to combine our suffering with Jesus' suffering on the cross. Scripture says that Jesus died once for all. I can't imagine that he didn't get the job done or that the redemption of the world requires some suffering from me in order to be complete. Surely not.
But there is a meaning for "offer it up" that is useful. What is offered to God, or sacrificed to God, is placed on the altar. It is literally "given to God" so that the person offering it no longer owns it; it now belongs to God. If we can offer our illness to God, place it on the altar and let him have it, then the sickness is no longer ours. We are free from it.
Perhaps we are hesitant to give him our illnesses. Why would he want to take them anyway? Yet we believe that he takes our sins, which are much worse than our illnesses.
Let us pray. Christ, my Redeemer, I give you today all the things that I have been holding on to that I don't need, don't want and can't handle.