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she describes the day as fun, but she doesn't think anybody likes her. When I ask why she tells me the above story in great detail.
My heart goes out to her! Your post shows several strong positives including her concern over whether others might get hurt, and her reflection about where things may have gone wrong and what she might do differently next time.

On one hand, anyone can have an occasional experience which turns into a comedy of errors. With practiced storytelling it can become a classic. On the other hand, she may not be very body-aware, and this lack of spatial awareness, along with inability to predict what will happen next, and inclination to divulge detail, may be possible signs of autistic spectrum disorder (ASD). Then again, it could just be symptomatic of being 6.

Because she seems concerned about friendships, she may enjoy having conversations with you over books with friendship tips, such as the children's books from Magination Press, free spirit publishing, and prufrock press.

Have you read the book, A Parent's Guide to Gifted Children? It provides insightful support for understanding, nurturing, and coaching gifted kids.