Haha, you're not far off. She's from Tokyo Ghoul, and the ghouls in it have black sclera and red irises when in "ghoul mode". She was born human but underwent a procedure to become a "half-human" so one of her eyes now works like a ghoul's.
The anime isn't great... For some reason they thought it would be a good idea to make seasons 1 and 3 cannon but season 2 non-cannon, yet they're all still considered to follow on from one another. The manga is better, but if you're not a manga reader then the anime is still worth a watch.
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