The Greek for 'come' refers to a constant or continuing action.
The kingdom of God has already begun, but we look for it to keep coming until it is here in all its fullness.
Healing is a part of God's kingdom.
That is why the Bible says that, when the multitudes came to Jesus, He received them and spoke to them about the kingdom of God, and then healed those who needed healing, Luke 9:11.
Later when Jesus sent the Seventy out to minister, He instructed them, "Whatever city you enter, and they receive you. . .heal the sick there, and say to them, 'The kingdom of God has come near to you.'"
Luke 10:8,9