Yume Kōjō: Doki Doki Panic (1987) by Nintendo Famicom Disk System game
Romhacking.net - Games - Yume Koujou: Doki Doki Panic
Doki Doki Panic Club by Karasu-96 on DeviantArt
Found an NES version of Doki Doki Panic on eBay! Thought it'd be a hack of the original sprites on top of Mario 2 but this appears to be the original game!