When you are viewing the song, at the top right just below the total song length is where the shuffle icon appears. It shows in blue when shuffle is active and white when it is not.
On the top left, just below the current time for the song is an icon with two arrows "chasing" each other. They are white when repeat is inactive, blue when repeat full playlist is active and blue with a tiny number "1" when repeat 1 song is active.
I suspect that you have the repeat 1 song option set. Tap that icon once more to turn it off. Then shuffle should work as expected.
Hope that helps.