"3 Praise be to the God and Father of our Lord Jesus Christ, the Father of compassion and the God of all comfort, 4 who comforts us in all our troubles, so that we can comfort those in any trouble with the comfort we ourselves receive from God." (2 Corinthians 1:3-4 (NIV))
So, as your friend stated you do have compassion. What drives your compassion for others? In particularly for those children in the hospital? Is it LOVE?
When asked what was the greatest commandment, Jesus responded that it is to love God with all our heart, mind and strength. But He added that the second commandment "is like it: 'Love your neighbor as yourself'" (Matthew 22:34-40).
We are not doing God work for him, as you put it. We are simply OBEYING his commandment and following HIS example which is to love and have compassion for each other.
It is pathetic that you need your God to command you to show compassion. You said "Consider the truth in Paul’s words—that God “comforts us in all our affliction so that we will be able to comfort those who are in any affliction” (2 Corinthians 1:4)." This statement says very clearly your God comforts us so that we in will be able to comfort others. Why does your God need our help to comfort others? Why doesn't he comfort them himself?