Acts 16:31 does not say “we only need to believe in Jesus” to be saved and need not fear sin or hell. It says “believe in the Lord Jesus and you will be saved…you and all your household…. (Note: “then immediately he and all his family were baptized”). “Faith is necessary for salvation. The Lord himself affirms: "He who believes and is baptized will be saved; but he who does not believe will be condemned" (Mk 16:16--- Catechism
no. 183). We also know from Scripture that without faith it is impossible to please God…and without faith no one has ever attained justification
, nor will anyone obtain eternal life ‘But he who endures to the end’ (ibid. no. 161).
And because “faith is an entirely free gift that God makes to man, we can lose this priceless gift as St. Paul indicated to St. Timothy: "Wage the good warfare, holding faith and a good conscience. By rejecting conscience, certain persons have made shipwreck of their faith." (Catechism of the Catholic Church
no. 162- 1 Tim 1:18-19. Cf. Mk 9:24; Lk 17:5; 22:32, Gal 5:6; Rom 15:13; cf. James 2:14-26]”
Like the prodigal son, we are free to lose our inheritance, and walk away from the Father. He is always there to receive us, but we must repent before we come home. For, “we cannot be united with God unless we freely choose to love him. But we cannot love God if we sin gravely against him, against our neighbor or against ourselves: "He who does not love remains in death. Anyone who hates his brother is a murderer, and you know that no murderer has eternal life abiding in him."1 John 3:15 ….To die in mortal sin without repenting and accepting God's merciful love means remaining separated from him for ever by our own free choice. This state …is called "hell." Catechism
Not only is there no scriptural evidence to support the belief that one can be saved without worrying about sin, there is no historical support for it either. If the assurance of salvation teaching is central in the Christian faith…then why had no one heard of it before the Reformation? We have thousands of manuscripts from the Early Church Fathers, and in them we find all the central teachings of Christ. Why is there no mention of assurance of salvation? Clearly, it was not taught by Jesus or his disciples.
So the next time someone asks you, “Are you saved?” You can say: "As the Bible says, I am already saved (Rom. 8:24, Eph. 2:5–8), but I’m also being saved (1 Cor. 1:8, 2 Cor. 2:15, Phil. 2:12), and I have the hope that I will be saved (Rom. 5:9–10, 1 Cor. 3:12–15). Like the apostle Paul I am working out my salvation in fear and trembling (Phil. 2:12), with hopeful confidence in the promises of Christ (Rom. 5:2, 2 Tim. 2:11–13)."
Recommended reading: The Salvation Controversy
by Jimmy Akin