Your willingness to humble yourself and openly confess where your tongue has failed is itself a work of grace, and God honors that honesty. An honest admission of weakness is far better than pretending all is well while the heart is still troubled. Scripture promises that if those who are called by His name humble themselves and pray and seek His face and turn from their ways, He will hear from heaven and forgive and bring healing. That promise is for you. Daniel modeled this when he was still praying and confessing his own sin and the sin of his people and presenting his plea before the Lord. John gives the same assurance that if we confess our sins, He is faithful and just to forgive and to cleanse us from all unrighteousness, and the proverb reminds us that the one who confesses and forsakes sin will find mercy.
You have quoted Paul's words that God's grace is sufficient and His power is made perfect in weakness, and that is exactly what you are experiencing. When we stop defending our own strength and gladly acknowledge our weakness, the power of Christ can rest upon us. That is why Paul could delight even in insults and hardships and difficulties, because when he was weak then he was strong through Christ. Your struggle with the tongue has brought you to that place of weakness, and faith is what allows God to make the weak strong. What is impossible with people is possible with God.
James shows us why this struggle feels so heavy. The tongue is a small member yet it boasts great things. It can kindle a fire that spreads like a forest fire, a world of wrong that can stain the whole life and set the course of life ablaze. With the same mouth we bless God our Father and we curse people who are made in the likeness of God. That inconsistency reveals what is inside us, and James is clear that no person on his own can tame it. It is restless and full of deadly poison. That is why your desire to simply push a button and be done with future stumbling can never be satisfied by willpower alone. Only the Holy Spirit can bring the tongue under control as we yield to Him. The highest use of this small instrument is to offer praise to God, and the same tongue should then be used to build up others, to comfort, to strengthen, to give hope and healing. A wise tongue uses knowledge well, while a foolish mouth pours out folly. A wholesome tongue is like a tree that gives life, but perverseness in it breaks the spirit of another. God wants your words to be healing.
Part of that healing comes through learning to be quick to listen and slow to speak and slow to become angry. There is an anger that is not sinful, such as anger at evil and injustice, as Jesus showed when He cleansed the temple and when He was grieved at hard hearts that would keep a man from being healed. But the anger of man does not produce the righteousness of God. Bitterness and wrath and anger and clamor and evil speaking grieve the Spirit and must be put away. The one who is slow to anger quiets strife and makes peace. Ask the Lord to give you that steady, gentle disposition, to renew your mind day by day, so that your responses are shaped by His Spirit and not by the flesh.
Confession is not meant to be done alone. James urges us to confess our sins to one another and pray for one another so that we may be healed, and he says the prayer of a righteous person is powerful and effective. David, when he was confronted about numbering the people, did not cover his sin. He admitted it and begged God to take away his iniquity, and there he found forgiveness and the wiping away of guilt. To cover sin brings no blessing, but to confess and forsake it brings mercy. Forgiveness in the kingdom is not a matter of counting how many times we must forgive, it is a matter of the heart. Love is patient and kind and keeps no record, and because we have been forgiven much we are called to extend that same long suffering to others.
The discipline you feel now, though painful at the moment, is not without purpose. No discipline seems pleasant at the time but afterwards it yields the peaceful fruit of righteousness to those who are trained by it. Even Jesus, the author and perfecter of our salvation, was perfected through suffering and learned obedience through what He suffered, becoming the source of eternal salvation. Your trials, as they teach you patience and endurance, can produce maturity and a quiet confidence and hope that does not disappoint, because God is gracious and compassionate, slow to anger and abounding in love, and He intends to work all things together for good for those who love Him.
Continue to take words with you and return to the Lord, asking Him to take away all iniquity and receive you graciously. Keep abiding in Christ and in His words, for His name alone is given under heaven by which we must be saved, and He is the one mediator between God and humanity. Pray in His name for grace to walk as He walked, to keep a pure heart and a good conscience and sincere faith, which is the goal of His command. He who began this sanctifying work in you, both the initial work and the ongoing work as you cooperate with His Spirit, will be faithful to complete it, until your tongue and your whole life more consistently become instruments of righteousness for His glory.