If you're a believer, don't worry - Satan, the Accuser of the brethren, will remind you constantly of your sin. But not the Holy Spirit. The Holy Spirit does not convict a believer of sin but of his RIGHTEOUSNESS because of Jesus' sacrifice (John 16:8-10). We are righteous not because of what we do but because of what HE did. "It is finished."
Romans 2: 14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law, 15 since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.)
But, more to the point, the Apostle John says "if we say we have no sin we deceive ourselves..."
Therefore, the Holy Spirit convicts our hearts of sin.
Jesus said in John 16: 7 But I tell you the truth: It is for your good that I am going away. Unless I go away, the Counselor will not come to you; but if I go, I will send him to you. 8 When he comes, he will convict the world of guilt in regard to sin and righteousness and judgment: 9 in regard to sin, because men do not believe in me; 10 in regard to righteousness, because I am going to the Father, where you can see me no longer; 11 and in regard to judgment, because the prince of this world now stands condemned. 12 "I have much more to say to you, more than you can now bear. 13 But when he, the Spirit of truth, comes, he will guide you into all truth. He will not speak on his own; he will speak only what he hears, and he will tell you what is yet to come. 14 He will bring glory to me by taking from what is mine and making it known to you. 15 All that belongs to the Father is mine. That is why I said the Spirit will take from what is mine and make it known to you. 16 "In a little while you will see me no more, and then after a little while you will see me."
It is for our good that God convicts our hearts of our sin. Our response is supposed to be that we "confess our sins" because "He is faithful and just to forgive us our sin and cleanse us from all unrighteousness."
That's the point! If you are NOT one of the brethren, Satan will leave you alone. What would be the point? If anything, he may do everything he can to make that person successful, just to show how "big a fool" a believer is. I've had people tell me that, I don't believe in God yet I make so much more money than you do, have a bigger house, drive a newer car...