I am sorry you've been abused by your cousin.
There's no specific way which is "right" in how we do or do not react to abuse.
You are not a bad person for not experiencing a "horrific" response to remembering.
Sometimes, we react to these events later in life. Sometimes, we deal with them earlier and the power they have over us tends to dissipate as we each regain our own sense of power.
If you continue to be bothered by feelings, flashbacks or are feeling overwhelmed by this, you may want to process this with a therapist?
You are courageous to share here. I hope you will feel more settled by having shared. Continue to post if you'd like, of course!

WC