Although it's a commonly accepted platitude, the Bible never says "forgive and forget".
But the Bible does say to "forgive as the Lord forgave you" (Colossians 3:13) and God says "I will forgive their iniquity, and their sin will I remember no more." (Jeremiah 31:34)
We know that God is omniscient - all-knowing - so he doesn't "forget" our sins, but He chooses not to remember them, not to dwell on them, not to hold them against us.
When God forgives us, it results in the complete removal of all estrangement and alienation between God and man.
It restores completely the relationship which existed prior to the sin.
We know this from the following verses:
". . . you have put all my sins behind your back." (Isa 38:17)
"You will again have compassion on us; you will tread our sins underfoot and hurl all our iniquities into the depths of the sea" (Mic 7:19)
" . . .For I will forgive their wickedness and will remember their sins no more" (Jer 31:34)
"As far as the east is from the west, so far has he removed our transgressions from us" (Ps 103:12)
Since the Bible tells us to forgive others, as the Lord forgave us, ideally this same result is attained in human forgiveness. We choose not to remember the offense and the relationship is restored which existed prior to the offense. This is true forgiveness - following God's example.
If we hang on to the memory of the offense, it is impossible to have a fully-restored relationship.
I think every situation is unique. There are other factors to consider, like the level of relationship prior to the offense and repentance, sincere, deep-felt sorrow for the wrong, on the part of the offender.
I know from personal experience how hard it is to forgive someone who has hurt you. It can take time and can be an emotional wrestling match within you.
But forgiveness is the essence of who Jesus is and who he called us to be. "For if you forgive other people when they sin against you, your heavenly Father will also forgive you." (Matthew 6:14)