Apple Music listening history
Its available to me off the menu in the header. click the menu icon, then click the clock icon in the pop-up.
Is there a bar on the bottom of the screen showing which song is currently playing?
If so you can try dragging that up and it should bring you to a screen that has more stuff on it.
Click on the button that looks like three dots with horizontal lines to the right of them (it's to the right of the skip/fast forward button);
that will show "Up Next" if you scroll up you will see your History.