Usually people write that budgies relax in the dark but mine is the exact opposite. She starts circling her cage and if she hears any sound close enough she starts screaming like a backtracking truck.

As I result I've resorted to leaving the blinds open so the moonlight enters the room and now she stays calm and doesn't scream if I happen to wake up in the night. The problem is I have trouble sleeping with lights and I frequently wake up and the worst that, on weekends, I end up waking up sooner than I'd want to as the sun shines on my face.

Does any of you think of a solution that might work to stop her from screaming in the dark?

She's just a few months old and I've only had her for a few days so I get she's scared but I still wonder if there's anything else I could try.

What I recomend is putting a blanket partly over her cage and adding a small nightlight to it.

Same thing happened with my budgie. She started having nightfrights every single night. She was incubating and was scared. 

For aa few nights everytime she screamed I used to switch on the light and pacify her. She turned out fine after a couple weeks. But if you want a quick solution I'd suggest what Skye Lily did