I'm a diabetic and I take insulin. Should I trust in God for my healing and not seek the aid of a doctor (II Chronicles16:12)?
Perhaps I should walk off of a cliff and trust that God will prevent me from being injured. Oh, wait a minute, someone suggested that before and it was roundly denounced. "Then the devil took Him up into the holy city, set Him on the pinnacle of the temple, and said to Him, "If You are the Son of God, throw Yourself down. For it is written: 'He shall give His angels charge over you,' and, 'In their hands they shall bear you up, Lest you dash your foot against a stone.'" Jesus said to him, "It is written again, 'You shall not tempt the LORD your God.'"" (Matthew 4:5-7). Man is not in the position to put God to the test.
God has never said that His followers should not go to doctors or to take medicine. Actually, quite the opposite, see "Physicians, Doctors, Healers." The problem arises when a person puts their sole trust in what man is able to accomplish. That was Asa's problem. "And in the thirty-ninth year of his reign, Asa became diseased in his feet, and his malady was severe; yet in his disease he did not seek the LORD, but the physicians" (II Chronicles 16:12). You are putting the emphasis in the wrong place. The problem is that Asa only would see the physicians and refused to seek the Lord's help. It was his refusal to seek help from God that lead to his early death. "Thus says the LORD: "Cursed is the man who trusts in man and makes flesh his strength, whose heart departs from the LORD"" (Jeremiah 17:5).
Just as man is expected to work for a living (II Thessalonians 3:10), but to also remember to thank God for the blessing of food on his table (Matthew 6:11), so should a man in all his life do what he is able to do and then lean on His God to make up for all his inadequacies.