Ephesians 2:13 says that we're brought near by the Blood of Christ. Colossians 1:20 says that He's made peace for all through the Blood of His Cross. 1John 1:7 says that if we walk in the light as He's in the light, we have fellowship one with another and the Blood of Christ cleanses us from all sin. 1Timothy 2:6 says that Jesus is the corresponding ransom for all men, but 2Corinthians 5:20 still indicates reconciling ourself to God and Romans 10:9 indicates confessing Jesus as your Lord from a heart that believes that God raised Jesus from the dead. Romans 10:10 says that with the heart this confession is made unto salvation.
A lot of folks that would come around here would balk at a "sinner's prayer" being written out, but all that those are, are a heart felt reaching out to the Lord and calling upon Him while He is near, according to Isaiah 55. Many would say that there's no mystical power to a particular set of words, per se, but Romans 10:9-10 get fairly specific. You've been growing in the understanding of Jesus as the Saviour of the whole world, especially of those that believe according to 1Timothy 4:10, but personally salvation is when you've embraced Him as your Saviour.
Acts 17 and Acts 20 indicate that we should both repent and have faith in our Lord Jesus. If you compare Revelation 3:20 with Ephesians 2:13 then you've got a better idea of the nature of the knocking that our Lord is doing on the door of your heart. Jesus taught to ask, seek, and knock because those that asked would receive, those that sought would find, and those that knocked would have the door opened to them. 1Peter 1:17-21 (I'd encourage you to read it) say that we're redeemed by the precious Blood of Christ. 1Peter 1:21 says something very similar to Romans 10:9:
Who by him do believe in God, that raised him up from the dead, and gave him glory; that your faith and hope might be in God.
1Peter 1:22 says that our souls are purified by obeying the truth, and verse 23 says that you're born again not of corruptible seed, but of incorruptible seed, through the Word of God which lives and abides. 1Corinthians 15 says that it's the resurrection of Jesus Christ that makes our salvation good. He said that if Christ Jesus isn't raised from the dead, then we would be dead in our sins without the hope of recovery.
If you believe these things, simply pray this prayer if you wish to know for certain on Scriptural grounds that you're a Christian:
Father, in the Name of Jesus, I believe that You've raised Jesus from the dead and I confess Him as the Lord of my life from this day forward, according to Romans 10:9. I believe that He was delivered for my offenses, and was raised again for my justification according to Romans 4:25. I believe that according to Romans 5:10-11 that I was reconciled to God by the death of His Son and that I am saved by His life, and not only so, but I also rejoice in God through our Lord Jesus Christ by whom we have received the universal reconciliation. I reconcile myself to You, according to 2Corinthians 5:20. Therefore, I am now Your righteousness according to 2Corinthians 5:21. Fill me with Your Holy Spirit, according to Romans 5:5, Ephesians 5:18, and John 17:22. I'll let the Word of Christ dwell in me richly in all wisdom, according to Colossians 3:12-17 in the Name of Jesus. I thank You, Father, that Your yoke is easy and Your burden is light. I now know for certain through the Scriptures and through the Holy Spirit that You give to those that obey You that I am a Christian. I thank You, Father in Jesus' Name for our reconciliation to each other. I know that I'm a New Creation in Christ according to 2Corinthians 5:17-21. I thank You, Father, that Jesus is the propitiation for my sin, according to 1John 2:1-2. Amen.