There is nothing in the Bible that mentions forgiving yourself. Such a concept is unbiblical and worldly. Forgiveness is from the one against whom you have sinned. Ultimately, when we sin, we sin against God and break his law. But also, sometimes our sin can be against another person when we break the Law of God. For example, if we lie to a person, we have sinned against God and that person, so we need to receive forgiveness from both.
To seek forgiveness from yourself would be to ask yourself to forgive you for what you've done against yourself. But this doesn't make any sense. We are not the ones who make moral laws that we can break. Rather, God does that, so forgiving yourself just doesn’t make sense.
The Bible tells us much about forgiveness, about forgiving each other, being forgiven by God, but never about forgiving ourselves.
Eph. 4:32, “And be kind to one another, tender-hearted, forgiving each other, just as God in Christ also has forgiven you.”
Colossians 3:13, “bearing with one another, and forgiving each other, whoever has a complaint against anyone; just as the Lord forgave you, so also should you.”
1 John 1:9, “If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.”
But, people feel guilty and need to be released
The idea of forgiving yourself carries with it the implication of guilt and the need to be released from the guilt. Sometimes we Christians do things that are truly regrettable, and the remnants of our sin haunt us. Usually it is in this context that someone might say a person needs to forgive himself, but again this is unbiblical.
Our forgiveness comes from God because ultimately it is God against whom we have sinned. If you are carrying guilt because of sin and you can't seem to get rid of it, then you need to realize that there is no sin you have committed that cannot be cleansed by the loving sacrifice of Christ. It is not an issue of your forgiving yourself. The issue is whether or not God forgives you. So, go to the cross and know that Jesus has already forgiven you, loves you, and will receive you to himself.