If you are talking about bodily healing then the Bible promises no such thing, even to the faithful. You see in 1 Timothy and 2 Timothy respectively that Timothy and Trophimus were faithful, godly men who were co-workers with the Apostles of Christ themselves, yet these men did not receive healing of the body. The teaching that such a thing is promised to Christians is indeed a great cause of needless anxiety and depression.
Now if you mean spiritual healing which consists of peace with God and dominion over sin, then that is something God has promised to whosoever will meet him on His terms in Christ. You must die to self and take Christ's yoke upon you that He might lead you and strengthen you to walk in the truth and righteousness of the requirements of God's Word. We must yield to Christ in surrender that He might reign over us and deliver us from our sins, since He died to redeem us from our sins that we might be His people who walk in His statutes and that He might be our God. Confess and forsake every wicked way in you that you know of, call on Christ to have mercy on you and deliver you from these, and go forward in following the good He requires that you know you ought to do. Study the Bible that you might understand His will more, know Him more, and walk in the light of His Word. The ultimate rest does not come until we do this faithfully until the end, but there is a measure of rest we can have here in the assurance by His Holy Spirit that we are indeed reconciled to Him by the blood of Christ and that we are on His side. If God be for us, then who can be against us? Being right with Him is worth more than having a healthy body, a good job, good relationships, and anything and everything else combined. What shall it profit a man if he shall gain the whole world and lose His own soul? Seek Him with your whole heart and you'll be on the right track in the most important thing- and He'll be faithful to at least provide anything else you truly need as you do so.
"28 Come unto me, all ye that labour and are heavy laden, and I will give you rest.
29 Take my yoke upon you, and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls. 30 For my yoke is easy, and my burden is light." (Matthew 11:28-30)
"29 Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent. 30 They said therefore unto him, What sign shewest thou then, that we may see, and believe thee? what dost thou work? 31 Our fathers did eat manna in the desert; as it is written, He gave them bread from heaven to eat.
32 Then Jesus said unto them, Verily, verily, I say unto you, Moses gave you not that bread from heaven; but my Father giveth you the true bread from heaven.
33 For the bread of God is he which cometh down from heaven, and giveth life unto the world. 34 Then said they unto him, Lord, evermore give us this bread. 35 And Jesus said unto them, I am the bread of life: he that cometh to me shall never hunger; and he that believeth on me shall never thirst." (John 6:29-35)
"24 Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed. 25 For ye were as sheep going astray; but are now returned unto the Shepherd and Bishop of your souls." (1 Peter 2:24-25)
"6 Seek ye the Lord while he may be found, call ye upon him while he is near:
7 Let the wicked forsake his way, and the unrighteous man his thoughts: and let him return unto the Lord, and he will have mercy upon him; and to our God, for he will abundantly pardon." (Isaiah 55:6-7)
"31 Therefore take no thought, saying, What shall we eat? or, What shall we drink? or, Wherewithal shall we be clothed? 32 (For after all these things do the Gentiles seek) for your heavenly Father knoweth that ye have need of all these things. 33 But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you." (Matthew 6:31-33)
