Basically, her story for that part should go like this.
- Get into the cave with Cecilia.
- Feed her bugs a few times/talk to her via quests.
- Reach the point where she doesn't want to eat bugs anymore
- Get to the part, where you have to feed more her "food" to recover her health - (You'll need to feed her something more than just bugs.)
- When you feed her enough food/fill her hunger bar up, she recovers some health the next day.
- You keep doing this until her health is 100%. Then an options appears to continue on with the story, when you interact with Cecilia.