Is it normal that i think i might have been molested as a child ?

Hello,

I am a 24 year-old straight women.
I just started therapy and was asked to do an autobiographical writing exercise of the main events in my life. As I wrote it, I realized that I don't recall much of my childhood, and the things I do recall are a little weird. They make me wonder if I could have been molested. Here are these weird things I remember :

1 - I remember, at 6, asking my baby-sitter if we could spoon for nap time. I remember the look on her face when I asked her that.
2 - At 7, I was playing barbies and all I did was making them have sex. I remember being aroused by this game.
3 - At 8, I had a phase when I kept making sex noises to be funny, with my baby sitter. She would find it weird and asked me where I had learned this. I don't remember my answer.
4 - At 7-8, I remember that I was sleeping at a friend's every monday, because we had soccer together. At night, I would turn every conversation we had into sexual stuff. Like, we would play roles of a couple and talk dirty. I always brought it on, not her. Again, it made me feel aroused.
5 - Since I've started being sexually active (very late, at 22), I found out that I have a fear of intimacy and that I find sex shameful. I feel gross, like if it wasn't right. I can't orgasm with a partner. I struggled with eating disorders and cutting throughout adolescence and early adulthood. I don't like being touched.

The thing is, the only memory I have that I think could be related to molestation is this one. It is quite incomplete :
I remember living in an apartment with my mom. I remember being very afraid in my room, but I don't know why. I think she had a boyfriend at that time but I can't recall his name or face. I don't even remember where was that apartment (and I do recall every other place where I've ever lived). I was between 2 and 6, I think. I recently read a book in which a woman tells her story about child molestation and when she described the abuse, I imagined her in that room (the one where I was afraid). I found it weird.

Do you think this is normal ? Is this just my imagination ? Knowing that I've been molested would sort of be a release, because it would mean that all of my suffering and troubles actually have a rational cause. But I don't want to create false memories. Please, tell me respectfully what you think.
Thanks a lot !