The name "album cover" implies that there is a "global" cover for an album and an album consists of more than one song. Mostly an image cover file is used for a complete directory of songs within. Your player treats your playlist like an album.
If you want different covers for each song ensure that there are no image files inside your music library directory structure. Or still better use a music player that supports different covers for each song even if there are album images inside. VLC music player is a very good choice available for free.
To reset album cover database simply delete the cache of your player. If player depends on Android's internal database delete Android's media cache/database (com.android.providers.media). You then have to wait until Android rebuild its internal database.