Luke, I would encourage you to look up verses dealing with assurance (and persuaded) - including the phrase, "full assurance." 1 John is an excellent book dealing with how we know we are Christians - through our obedience, love for the truth, love for the brethren, etc. If you came to the Lord the way He commands us to in His Word, then you should have that assurance.

First of all, it is the Holy Spirit that bears witness with our spirit:

Romans 8:16 The Spirit itself beareth witness with our spirit, that we are the children of God:

1 John 5:10 He that believeth on the Son of God hath the witness in himself: he that believeth not God hath made him a liar; because he believeth not the record that God gave of his Son.

We also get assurance through our obedience and closely walking with the Lord:

1 John 3:19-22 And hereby we know that we are of the truth, and shall assure our hearts before him. For if our heart condemn us, God is greater than our heart, and knoweth all things. Beloved, if our heart condemn us not, then have we confidence toward God. And whatsoever we ask, we receive of him, because we keep his commandments, and do those things that are pleasing in his sight.

If there is sin you are deliberately holding onto - or even an area of your life, where you know God's will but refuse to do it - then you will not have that assurance God wants to give you.

Isaiah 32:17 And the work of righteousness shall be peace; and the effect of righteousness quietness and assurance for ever.

Full assurance - entire confidence, completely assured. To be full of something Biblically means to be influenced or controlled by it. Full assurance is where your daily conduct is influenced by your assurance of your right standing with the Lord, your inheritance in Him, etc.

Full assurance of understanding - knowing the riches you have in the Lord Jesus Christ:

Colossians 2:2-3 That their hearts might be comforted, being knit together in love, and unto all riches of the full assurance of understanding, to the acknowledgement of the mystery of God, and of the Father, and of Christ; In whom are hid all the treasures of wisdom and knowledge.

Ephesians 1:17-19 That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him: The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints, And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power,

Full assurance of hope - filled with the confident expectation that the Lord will reward your service to Him, and will keep all His promises to you - in light of that you persevere when the going gets tougher:

Hebrews 6:9-12 But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak. For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister. And we desire that every one of you do shew the same diligence to the full assurance of hope unto the end: That ye be not slothful, but followers of them who through faith and patience inherit the promises.

Full assurance of faith - this is the assurance that comes through prayer, coming before the throne of grace - through the blood of Jesus, not your own good deeds or righteousness.

Hebrews 10:19-25 Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh; And having an high priest over the house of God; Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water. Let us hold fast the profession of our faith without wavering; (for he is faithful that promised And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching.

Ephesians 3:12 In whom we have boldness and access with confidence by the faith of him.

This is one of the verses that came up in my Bible program while I was searching for related passages:

2 Peter 1:10 Wherefore the rather, brethren, give diligence to make your calling and election sure: for if ye do these things, ye shall never fall:

This verse is part of a passage on the Christian continuing to grow in seven areas. Please consider this study, as it might be of some help to you: Precious And Growing Faith