I am agonizing over something that happened to me when I was a child, before I was 11 years old. I'm almost certain that what happened to me was sexual molestation. I blame myself and punish myself since I feel responsible in part for initiating the abuse or even enjoying it. Was I sinning if I partly enjoyed the abuse? I had free will, after all. And if I am partly to blame, could you show me biblically that God does not want me to punish myself for what I did?
You are not at fault for what was done to you at such a tender age. Of course you did have free will, but the will of a child is different than the will of an adult, given the limitations of the child's knowledge and his/her fear of adult power.
The Bible speaks to your situation. God's desire for us is to live guilt-free (Rom 8:1; 1 John 3:19-24). There is no condemnation in Christ. It's easy to forget this vital truth, especially when something in our past was so painful, shameful, or embarrassing. Let it go. I know you can’t let it go fully -- the memory persists -- but at least you can prevent it from dominating your thoughts.