Promise to Hold You Close.
Rin starts going crazy soon after Obito dies. It's innocent enough that no one, not even Kakashi, notices at first. She starts washing her hands every time she can, desperate to get blood that no one else can see from her hands.
After a few months of that, Kakashi belatedly notices that when she talks to him, she doesn't look at his face, even though he wears his hitai-ate over the scar and the eye that Obito inherited him with all the time.
When they start fucking - because they cling to each other despite everything else, because they're all each other have and they know they're incomplete and it's hard to carry on like that - she keeps her eyes closed, and when she comes it's almost as if it hurt her. Later she takes three or four baths and when she comes out, her skin is pink and raw and she keeps avoiding his eyes. Soon after that, she starts muttering to herself.
Rin dies on a mission the night of her seventeenth birthday. Kakashi is too far away from her to do anything; he only gets to see how, after she disposes of a ninja, Rin starts searching for some water to wash her bloodied hands, lips moving as she mutters to herself, and one of the enemies goes after her and cuts her throat from side to side.
Rin doesn't get to scream as she dies. Kakashi is the one that feels the scream closing his throat as he carries her body back to Konoha.