I don't think it was her words today that will him surrender. He had already said to her from the beginning that he would take whatever punishment she wanted to give to the culprit. So that's what he's doing now. He's not against her finding out about the truth per se, rather he doesn't want it leading up to Keerti. If the offender hadn't been his family member he would have probably hunted him or her down on Pallavi's behalf and put them behind bars by now.
But what can raghav acheive by surrendering himself pallavi already knows who is culprit how can she get closure when culprit is free infront of her and loosing her husband(raghav) again who is innocent
again she will become target of societal taunts