In the Gospel of Luke, chapter 7 verses 36 through 50, Jesus tells the woman she is forgiven even though it is not clear from the story that she confessed her sin. Her tears made a convincing demonstration of her need for God's love and redemption.
She connected to God's love.
When we repent, we are transformed by God's redeeming love. Strangely, we could turn back to sinning without losing our redemption; God's gift of forgiveness is eternal. Although we are all sinners, and we will sin, nevertheless we will work to avoid sin. One sign of the transformation is that what hurts the heart of God also hurts us. We feel pain if we sin. We have seen the love God has for us. It breaks our hearts to hurt the God who loves us so much.
If you need to see a sign in yourself that you are saved, I think this may be it. How much do you hurt when you sin? Does your heart ache for the pain you caused the Creator? If you can answer this, then you know.
From Gospel of Luke:
One of the Pharisees asked him to eat with him, and he went into the Pharisee's house, and took his place at table. And behold, a woman of the city, who was a sinner, when she learned that he was at table in the Pharisee's house, brought an alabaster flask of ointment, and standing behind him at his feet, weeping, she began to wet his feet with her tears, and wiped them with the hair of her head, and kissed his feet, and anointed them with the ointment.
The rest of the story
Now when the Pharisee who had invited him saw it, he said to himself, "If this man were a prophet, he would have known who and what sort of woman this is who is touching him, for she is a sinner."
And Jesus answering said to him, "Simon, I have something to say to you." And he answered, "What is it, Teacher?"
"A certain creditor had two debtors; one owed five hundred denarii, and the other fifty.
When they could not pay, he forgave them both. Now which of them will love him more?"
Simon answered, "The one, I suppose, to whom he forgave more." And he said to him, "You have judged rightly."
Then turning toward the woman he said to Simon, "Do you see this woman? I entered your house, you gave me no water for my feet, but she has wet my feet with her tears and wiped them with her hair. You gave me no kiss, but from the time I came in she has not ceased to kiss my feet. You did not anoint my head with oil, but she has anointed my feet with ointment. Therefore I tell you, her sins, which are many, are forgiven, for she loved much; but he who is forgiven little, loves little." And he said to her, "Your sins are forgiven."
Then those who were at table with him began to say among themselves, "Who is this, who even forgives sins?"
And he said to the woman, "Your faith has saved you; go in peace."
Luke 7:36-50 (RSV)