I've had sessions intensify the urges. I've also hurt myself in session without realizing it until it was pointed out to me. I have never cut in session, but have scratched myself as a way of self-soothing during a difficult session. At the time, my T pointed it out and asked about it. We were able to identify some triggers and talk me through it.
As almost everyone has said, it's probably a good time to bring up the topic with T. I understand puzzle_bug's hesitation though also, as I hate even remotely coming off as manipulative, but as one T put it, if it's honest in the moment, it's not manipulative. They are there to help us through our struggles, so it makes sense to ask for that help especially if they are available.