Since I keep on falling back into sin further and further, repeatedly. Does that mean I don't have a real determination to change? I want to change, yet I find myself just behaving worse than before. What should I do?
There are a few possibilities.
The most likely problem is a lack of encouragement. God understood that battling sin is hard and it is even harder if a person tries to battle it on his own. "Let us hold fast the confession of our hope without wavering, for He who promised is faithful. And let us consider one another in order to stir up love and good works, not forsaking the assembling of ourselves together, as is the manner of some, but exhorting one another, and so much the more as you see the Day approaching" (Hebrews 10:23-25). So many people see attending worship services as optional, but it serves as a critical element in our battle against sin. Being with other Christians recharges our batteries so we can continue the struggle against sin. Each Christian is battling their own set of problems, but just knowing that others are out there and making progress helps you with your own progress. "Be sober, be vigilant; because your adversary the devil walks about like a roaring lion, seeking whom he may devour. Resist him, steadfast in the faith, knowing that the same sufferings are experienced by your brotherhood in the world" (I Peter 5:8-9).
An important point to remember is that sin isn't unique to any one person. Lots of other people go through or have gone through the same struggles you are facing. "No temptation has overtaken you except such as is common to man; but God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will also make the way of escape, that you may be able to bear it" (I Corinthians 10:13). This is why God also encourages Christians to seek out wise advice from someone they trust, to gain personal help and encouragement. "Confess your trespasses to one another, and pray for one another, that you may be healed. The effective, fervent prayer of a righteous man avails much" (James 5:16). Knowing that someone is on your side, cheering you on, and praying for your success is a great help.
Another problem can be a lack of discipline. We often make it too easy to fall into sin, making excuses why reasonable hindrances to sin can't be put into place. We are supposed to resist the devil, but often it isn't much of a fight. Paul described it as a battle for which we must be properly equipped: "Finally, my brethren, be strong in the Lord and in the power of His might. Put on the whole armor of God, that you may be able to stand against the wiles of the devil. For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places. Therefore take up the whole armor of God, that you may be able to withstand in the evil day, and having done all, to stand. Stand therefore, having girded your waist with truth, having put on the breastplate of righteousness, and having shod your feet with the preparation of the gospel of peace; above all, taking the shield of faith with which you will be able to quench all the fiery darts of the wicked one. And take the helmet of salvation, and the sword of the Spirit, which is the word of God; praying always with all prayer and supplication in the Spirit, being watchful to this end with all perseverance and supplication for all the saints" (Ephesians 6:10-18). So inspect yourself and see if you are properly and completely equipped. Look at the situations when you do sin and ask yourself what can be done to make it harder to sin.