Healing is a two-way street. It is available to everyone because Jesus "went around doing good and healing all" (Ac 10:38). "The people all tried to touch him, because power was coming from him and healing them all" (Lk 6:19). But you have to be open to accept the healing. You can't have a closed mind. For example, Jesus made a trip to the town where he was born and raised. The people remarked "Isn't this the carpenter?" (Mk 6:3). Then "they took offense at him" (:3). Consequently "he could not do any miracles there, except lay hands on a few sick people and heal them" (:5). It is more than just a lack of cooperation. "Jesus began to denounce the cities in which most of the miracles had been performed, because they did not repent' (Mt 11:20). Few allowed miracles in Nazareth. Jesus was saying "it will be more bearable for Tyre and Sidon on the day of judgment than for you" (:22). He was "amazed at their lack of faith" (Mk 6:6) of the people in his hometown.
You've heard "necessity is the mother of invention." If you are sick you have a motivation to become well. If there is hope for a cure you optimistically take advantage of the opportunity. "A man with leprosy came and knelt before him and said, "'Lord, if you are willing you can make me clean'" (Mt 8:2). A centurion asked for help saying, "'Lord, . . . my servant lies at home paralyzed and in terrible suffering'" (:4). "A ruler came and knelt before him and said, "'My daughter has just died. But come and put your hand on her, and she will live'" (9:18). "Two blind men followed him, calling out, 'Have mercy on us, Son of David!'" (:27). "Ten men who had leprosy met him . . . and called out in a loud voice, 'Jesus, Master, have pity on us!'" (Lk 17:!3). Notice that they all had confidence in who he was and that he was capable of healing them.