Legend of Kyrandia 2: Hand of Fate?
More or less fits the bill...
No, that's not it.
I've been trying to think of more things I remember.
- I may have only ever played the demo version, and if I did, it think it came on a PC demo disc (perhaps one from PC Gamer?) that also had one of the early Heroes of Might & Magic games on it (but perhaps I'm mis-remembering, and that was actually a different disc?).
- I also remember the game starting in a little witch's hut.
- I don't think there were any other characters with you inside the hut. (but I could be wrong about that)
- I feel like the character sprites were also somewhat bigger than Legend of Kyrandia's. Something around the size of Strider's character sprites on the Genesis.
- I also remember the witch having a black outfit.
- In the beginning, after leaving your hut, you would travel from left to right.
- The more I think about it, the less I'm sure that it was an adventure game. I don't remember much action, and there seemed to be a decent focus on story. However, I don't remember many puzzles, and I think you had direct control of the character? It may have been some kind of platformer, but I also don't remember any floating platforms or anything.
Oh man, Hand Of Fate was going to be my guess as it's pretty much exactly what you described.