[there had been one person after another] - repeated infidelity (if this is about a relationship)
[it was like part of her would bust in a hundred pieces.] - she was badly hurt each time, though this doesn't connect very well with the previous sentence, which implies she didn't know
(flying-jinny) - merry-go-round (fairground ride with wooden horses going up and down and turning in a circle)
[the eyes walled blind and frantic.]- persumably, the horse hasn't been painted recently, so it isn't bright and shiny, and its eyes look dead and and a bit scary.