Some ppl above said good points already, with light source and thinking of the character as if they were in 3d space and the emotion/mood/personality you're trying to capture. Drawing orthographic views can give you a better grasp when thinking of your character in 3d space (well pseudo 3d space as it's a 2d drawing XD)
Search "orthographic character sheet" for references on making one if it's something new to you
From your drawing, shadow under her eyes now look as if her eyes are bulging out
I googled 'Anime Forehead shadow' and got results like this might serve as referance-
the example below, the edge-work on the shadow isn't too sharp and maintains that human roundness of the face:

and the character's personality/ expression you're trying to capture plays a part too, in the ones below the eyes to make the character look intimidating. Environment lighting is a major factor too, this guy below is lit from behind towards his right side -the source being the light from the celing (you can see the glow on the roof).
To me without the eyes usually work good for expressing mystery and disappointment (like that saying of someone feeling left in the dark) and the eyes visible works for intimidating and shocked characters. Eyes opened wide works good for the shocked or fierce while squinted eyes for the intimidating/ cold look.
But then again art is always flexible beyond my interpretations above lol The shadowed out eyes of the guy below gives me a mystery sense (the eyes are usually the 1st thing that draws a viewer so with that gone it gives the impression that the character's thoughts are mysterious/beyond our knowledge). His smile is what sells his expression here, he's clearly confident or maybe finds a little humor based on whatever he's thinking.

Guess that's a good exercise too, examining art that execute techniques you want to master, What impressions you get from the character/scene as a viewer? and figuring out how they achieved it 
For me when it came to lighting, looking at Scene lighting tutorials for photography and film on YouTube were helpful.
A photography example from youtube, he mentions mood too
Horror is usually my jam for their high contrast lighting, looking at stills from horror movies and games can be inspiring too in the way they manipulate the viewer to see certain things within a scene or even on a character's body.
hope this serves some help, keep up the hard work 