Is healing up to God alone? It isn't God who decides who gets healed and who doesn't. For instance, it's not God's will for anyone to perish, but they do according to 2 Peter 3:9 "The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance." God doesn't force salvation on anyone, but it is available to anyone as it says in John 1:12 "But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name."
God has already provided healing for everyone at the whipping post so healing is an accomplished work that must be received by faith. But not everyone is healed. When He died and said that "It is finished", He meant that his work on earth was finished. The atonement was complete for our salvation and healing was complete at the whipping post. Just like God is waiting on us to receive Jesus as savior, He is waiting on us to receive healing based on our faith in what Jesus did at the whipping post for us. It is just a simple matter of receiving what He has already done for us according to 1 Peter 2:24 "Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed."
It's already a done deal. We do not pray for healing in our ministry. We command the healing that God has already provided. Since God provided healing 2000 years ago, and we don't have it yet, that means something is hindering the healing. In the first place, healing is hindered by the fact that we don't know what is available for us [lack of knowledge per Hosea 4:6].
In the next place, we find that Satan may be involved in preventing the healing, either as directly involved in the sickness, such as Matthew 12:22 "Then was brought unto him one possessed with a devil, blind, and dumb: and he healed him, insomuch that the blind and dumb both spake and saw." or by trying to prevent the healingas shown below: