What does the Bible say about mental-health disorders?

While we cannot offer personal counseling specifically concerning your child, we can assist you to better understand biblical demon-possession vs true mental-health disorders.

First and foremost  we must make clear that once a person becomes a Christian, they are no longer susceptible to demon-possession, though the enemy can still tempt, deceive and influence in negative ways when we live in the flesh and not in the Spirit. 

Furthermore, we must look at the scriptures to understand specific behavior patterns to watch for in a demon-possessed human: 

MATT. 9:32 And as they were going out, behold, a demon-possessed man who was unable to speak was brought to Him. 
MATT. 9:33 And after the demon was cast out, the man who was previously unable to speak talked; and the crowds were amazed, and were saying, “Nothing like this has ever been seen in Israel.” 

MARK 5:1 They came to the other side of the sea, into the region of the Gerasenes. 
MARK 5:2 When He got out of the boat, immediately a man from the tombs with an unclean spirit met Him. 
MARK 5:3 He lived among the tombs; and no one was able to bind him anymore, not even with a chain, 
MARK 5:4 because he had often been bound with shackles and chains, and the chains had been torn apart by him and the shackles broken in pieces; and no one was strong enough to subdue him. 
MARK 5:5 Constantly, night and day, he was screaming among the tombs and in the mountains, and cutting himself with stones. 
MARK 5:6 Seeing Jesus from a distance, he ran up and bowed down before Him; 
MARK 5:7 and shouting with a loud voice, he *said, “What business do You have with me, Jesus, Son of the Most High God? I implore You by God, do not torment me!” 
MARK 5:8 For He had already been saying to him, “Come out of the man, you unclean spirit!” 
MARK 5:9 And He was asking him, “What is your name?” And he *said to Him, “My name is Legion, for we are many.” 
MARK 5:10 And he begged Him earnestly not to send them out of the region. 
MARK 5:11 Now there was a large herd of pigs feeding nearby on the mountain. 
MARK 5:12 And the demons begged Him, saying, “Send us into the pigs so that we may enter them.” 
MARK 5:13 Jesus gave them permission. And coming out, the unclean spirits entered the pigs; and the herd rushed down the steep bank into the sea, about two thousand of them; and they were drowned in the sea.

MARK 9:17 And one person from the crowd answered Him, “Teacher, I brought You my son, because he has a spirit that makes him unable to speak; 
MARK 9:18 and whenever it seizes him, it slams him to the ground, and he foams at the mouth and grinds his teeth and becomes stiff. And I told Your disciples so that they would cast it out, but they could not do it.” 
MARK 9:19 And He answered them and *said, “O unbelieving generation, how long shall I be with you? How long shall I put up with you? Bring him to Me!” 
MARK 9:20 And they brought the boy to Him. When he saw Him, the spirit immediately threw him into convulsions, and falling to the ground, he began rolling around and foaming at the mouth. 
MARK 9:21 And He asked his father, “How long has this been happening to him?” And he said, “From childhood. 
MARK 9:22 It has often thrown him both into the fire and into the water to kill him. But if You can do anything, take pity on us and help us!”

ACTS 16:6 It happened that as we were going to the place of prayer, a slave woman who had a spirit of divination met us, who was bringing great profit to her masters by fortune-telling. 
ACTS 16:17 She followed Paul and us and cried out repeatedly, saying, “These men are bond-servants of the Most High God, who are proclaiming to you a way of salvation.” 
ACTS 16:18 Now she continued doing this for many days. But Paul was greatly annoyed, and he turned and said to the spirit, “I command you in the name of Jesus Christ to come out of her!” And it came out at that very moment.

As we read these scriptures we begin to see that a person who is demon-possessed has very distinct behavior; an inability to speak, super-human strength, uncontrollable screaming, hurting oneself (even to the point of death), convulsions, suicide, and the ability to know things outside human understanding. These are trade-mark demonic behaviors within a human being, which can look like mental illness in some cases. The enemy and his demons may inhabit the body of any unbeliever as the Lord permits, and by that indwelling may manipulate and control them causing them to do many violent and extreme things which is usually attributed to mental illness by the unbelieving world. 

While demon-possession is possible in some cases, it is unlikely to be the cause for the majority of mental-illness cases we see today within families. Should someone be diagnosed with obsessive-compulsive disorder (OCD), anxiety, and/or autism we would suggest seeking professional help. Thus being said, serious cases of mental-illness may benefit from medicinal therapy, further persuading us that this person is in fact struggling with "real" mental-illness and not demon-possession. 

When God calls a believer to care for someone with mental-illness, this come with great responsibility, as well as the need for complete surrender, strength, and daily guidance. When God places a child in our care that needs more help, we must be ready to shower that child with prayer and continually share the Gospel whether they respond or not. God is still sovereign over the salvation of a child with mental-illness. In most cases this is life-long task to bear but it doesn't come without significant reward in eternity as we see in scripture:

JAMES 1:2 Consider it all joy, my brothers and sisters, when you encounter various trials, 
JAMES 1:3 knowing that the testing of your faith produces endurance. 
JAMES 1:4 And let endurance have its perfect result, so that you may be perfect and complete, lacking in nothing.

JAMES 1:5 But if any of you lacks wisdom, let him ask of God, who gives to all generously and without reproach, and it will be given to him. 
JAMES 1:6 But he must ask in faith without any doubting, for the one who doubts is like the surf of the sea, driven and tossed by the wind. 
JAMES 1:7 For that person ought not to expect that he will receive anything from the Lord, 

Through the words of James, God comforts the believer who encounters various trials and tests in this life. He lets us know that trials and tests actually produce a more mature walk with Christ, through endurance and perseverance. Should any of us lack wisdom when going through these trials, whether life-long or life-altering, if we ask for wisdom, God will give it. This doesn't mean some of the time or most of the time God will give you wisdom to trek through a trial, but always. 

On the other hand, while Christians cannot be possessed by demons, this is not to be confused with being persuaded or influenced by one. For example King Saul was tormented by evil spirits when he rebelled against the Lord:

1SAM. 16:14 Now the Spirit of the Lord left Saul, and an evil spirit from the Lord terrified him. 
1SAM. 16:15 Saul’s servants then said to him, “Behold now, an evil spirit from God is terrifying you.

Further, all throughout the New Testament we see believers plagued with torment by the enemy, most notably Paul:

2COR. 12:7 Because of the extraordinary greatness of the revelations, for this reason, to keep me from exalting myself, there was given to me a thorn in the flesh, a messenger of Satan to torment me—to keep me from exalting myself!
2COR. 12:8 Concerning this I pleaded with the Lord three times that it might leave me.
2COR. 12:9 And He has said to me, “My grace is sufficient for you, for power is perfected in weakness.” Most gladly, therefore, I will rather boast about my weaknesses, so that the power of Christ may dwell in me.

We must rest on the promises of scripture; that if we resist the enemy's efforts to lead us astray, he will eventually flee:

JAMES 4:7 Submit therefore to God. Resist the devil and he will flee from you. 

As a believer, resisting the enemy doesn’t mean actively fighting him but rather it means not giving in to his temptations. 

In summary, we should not fear the enemy but neither should we imagine we have power against him. When we see someone possessed by the demonic realm, we should understand that the person is not our enemy, since our enemy is not flesh and blood. Nevertheless, we should not attempt to fight the power of the demon inside the person by our power. Should the Spirit direct us in some way against the person, then we should obey and operate in the Spirit. Otherwise, we should act wisely by resisting any temptation of the enemy to respond in anger, hatred or pride.

You may find the following articles on our website further help in your situation:

The role of medicine vs. faith
Is epilepsy connected to demon possession?
How do I respond to a demon-possessed person?

Additionally, we highly recommend listening to our Joy in Suffering teaching and/or our James teaching online to help you discern your situation.

Scripture quotations taken from the (NASB®) New American Standard Bible®, Copyright © 1995, 2020 by The Lockman Foundation. Used by permission. All rights reserved. www.lockman.org