This question does not really fit the criteria for here, but here are a couple of suggestions anyway. First, your recollections of that 4-year-old sermon may be partially incorrect, plus the speaker may have added a few points that may not actually be in the Bible. Therefore, I have two possibilities to offer.
First, Mark 5:24-34. However, this lady was Jewish, nor did she ask for forgiveness. She expected healing, surreptitiously touching the hem of Jesus' garment in a pressing throng. She was instantly healed, but Jesus stopped to find out who had carried out that act of faith, causing her to come forward to admit it, and she was terrified. But Jesus was really kind to her, saying, "Daughter, your faith has healed you. Go in peace and be freed from your suffering."
Second idea, Matthew 15:21-28 - the most likely one. This was a Syro-Phoenecian woman (a Gentile) and the location was the region of Tyre and Sidon. She cried out to Jesus, "Lord, Son of David, have mercy on e! My daughter is suffering terribly from demon-possession." At first, Jesus ignored her and the disciples urged him to send her away, as she kept crying this out. Jesus then said that he was sent to the lost sheep of Israel. She knelt at his feet, again asking for help. He tested her by then saying, "It is not right to take the children's bread [Israelites] and toss it to the dogs [Gentiles]." She agreed but added (in faith) that even the dogs [like herself] get to eat the crumbs fallen from the [Israelite] table.
At that, Jesus said she had great faith, so her request was granted. Her daughter was healed from that very hour.
I think the reason you could not find the actual account is that you wrongly thought she was asking for forgiveness, when in both these cases, the women had faith for healing. But the second account fits the bill of a Gentile woman.