Yes this is a big question. Where are the hands that actually heal? In the church, we have seen it both ways: If we pray for them and they don't get healed, then it is because of our lack of faith. If they pray for us and we don't get healed, it is because of our lack of faith. :) Just being humorous as it always seems to come back to our faith.
I have seen people instantly and miraculously healed, and then so many others that were not. I do not understand the huge variance. Jesus plainly said that the words you quoted there: "whatever you ask for in prayer, believe that you have received it, and it will be yours" and we know that Peter walked on water until he began to doubt. James said let them ask of God, not doubting. All that I know to do is to keep praying until it happens. For while I breathe, there is hope.