During this life that we live on earth God won't heal everyone of their problems and sickness. People suffer. People die. That won't ever change.
However we, as christians, can find peace in God that the day we die, we will be instantly healed of every little problem we had.
I'm not saying that God will never heal the sick, or help those that are sick or injured to have a full recovery. When he does, it is a testiment to His power and glory. One that we can use to show to the world of His power and glory.
In Job, God let Job suffer through the loss of his friends and family, the loss of his flocks and servants, and finally the loss of his health. Though he suffered severly and his friends tried to make him denounce God's name Job remaned strong and never sinned against God. His life and struggles was left as a testiment of his faith in God. Which is exactly what those who suffer on this earth can do.
All of the disciples suffered and died horrible deaths in the name of Chist.
Stephan was stoned. And the list goes on and on.
I will always consider it a blessing and an honor to suffer in God's name so that others can see the size of my faith and the size of my God.
Also if you say its the strength of your faith in God that heals you, what of those that constantly suffer and are strong christians? Are you going to jugde them and say they need to believe more? I suffer constantly from a mustle disease, is that becuase I don't have faith enough? I don't think so. Saying that is one of the worst things you would ever say to someone who is in pain of suffering. You tell them they need to believe more and you will start a darkness in their hearts that presses them further from God.
As for healing, not everyone has the ability to heal or cast out demons. Those are gifts that are God given. In the bible(not sure the verse, sorry) it says that God has given everyone a gift. There are a list of 8 or 9 of those there. Theres the gift of prayer, faith, healing, preaching, among others. Sometimes you can have more than one but not everyone has the same gifts.