There are times when we must suffer for others as part of God's plans, the working out of God's will.
2 Corinthians talks about Christian service, from the viewpoint of a Christian servant. Paul had the sentence of death on him as well - suffering for the purpose of saving and delivering people. We should not trust in ourselves but in God who raised us from the dead - the burden is too great for us, and as sinners there is nothing we can do for God's service except/unless He raises us and gives us new life, new abilities and energies; not human talents but spiritual gifts that only come as a result of God's work in us.
We comfort others - we channel God's comfort to others by speaking of our sufferings; it can also come from us being encouraging examples as Christians who suffer but continue to persevere. Modern society incapable of producing people of true endurance? Christian martyrs of the past - what effects did their deaths and sufferings have on Christianity in England? What kind of men are these? They suffered without hate or defiance, calling on God to receive and forgive their tormentors. These are the sufferings of Christ, and it is a privilege to be identified with Him by suffering similarly. Peter died in the same way as Jesus - except he asked to be crucified upside-down, perhaps because he did not feel worthy of dying in the same way as Jesus.
A simple promise that our sufferings glorify God is enough - we don't have to know exactly how it is worked out. Behind this there is joy - He is our comforter, our father of mercy; the promise of deliverance - He has and continues to deliver us, in this life or otherwise. We will not back down even if He doesn't deliver us in an immediate or obvious way.