Shuffle sorta works...

My music shuffles, but not really, if you know what I mean. I have over 1800 songs in my music library, but I can hear the same song several times over the course of a couple of days. Why does this happen?

Because that's what "random" means. It is statistically possible for shuffle to play an entire album in the album order. And, it's possible to hear the same song more than once in a couple of days. As I understand it, every time you start playing, things are re-shuffled.

I used to do a lot with smart playlists in iTunes (and then sync them to my iPhone). You can set the smart playlist so that it won't play things that have been played in less than a certain amount of days.

Create a Smart Playlist in iTunes on Mac - Apple Support

You might also check to make sure you don't have more than one version of the same song.