I have a story for you: A man swept away by a flood sees two guys approach in a rowboat. "Hop in!" they shout. "No, thanks," he says, "God will save me." Next, a tugboat passes by. "Climb aboard," calls the captain. Again he refuses. "God will save me," he says. Then the Coast Guard sends a helicopter but he refuses to board, giving the same reason. Finally, he drowns.
Up in Heaven, an angel asks why he refused help. "I wanted to rely on God alone," he replies. "Idiot!" says the angel. "Who do you think sent you the rowboat, the tugboat and the helicopter?"
God acts through the guise of doctors and medicine, just as He acts through the guise of employers to provide us with a living. Would your friends refuse to take money from their bosses, saying they'll get it directly from God? I think not. Do they eat food, or do they wait for God to miraculously inject their bloodstream with nourishing vitamins, minerals, fats and carbohydrates?
The Torah (Bible) gives explicit permission to engage in healing: If one person strikes another person, the verse says that the attacker "shall pay for his unemployment and for his medical expenses." (Exodus 21:19)
Our task is to exert the effort and then to recognize that ultimately it is God who heals. While seeking proper medical attention, a sick person simultaneously engages in prayer, good deeds, and introspection. We don't accept prayer as "a last resort" --it's a "first resort," along with medicine and the doctor.