I read this book in the late '70s, years before I came across Norma Fox Glazer's Saturday, the 12th of October.
This protagonist is a girl in her early teens who's insecure and not popular. One Saturday (I think), she has a big fight with her brother, and I don't know exactly what happens, but she finds herself in a big meadow sitting/reclining at the edge of a stream. Somehow she knows that she's in prehistoric times.
Sitting at the stream, she becomes aware that something is staring at her, and the Thing is staring so intensely that it feels like its eyes are burning holes in her back. She is terrified when she actually finds two burns on her back. A group of prehistoric people is passing by, so she joins them to escape the Thing.
I don't remember how much time she spends with the prehistoric people, but when she gets back to her own era, no time has passed. Relieved, she thinks she must have been dreaming, but she still has the burns on her back. She also senses that the Thing may have followed her to the present. That's all I can remember.