I wanted to do this in digital but I don't have the time right now.
For context I hc Rin and Obito as 2 years older than Kakashi, so Kakashi was 12 during Kannabi and Rin and Obito 14.
I don't usually draw Rin that much but I absolutely love her and plan to do more with her. It's funny because when I first watched the show I didnโt like her. It wasn't until I began to read fanfics and saw all the headcanons and interpretations of her character here on tumblr that I started to like her. So thank you all for that <3<3
So here are some (bits of how I see her/of my my headcanons about her) on her relationship with Kakashi.
Rin used to idealize Kakashi, so ended up crushing on him. And Kakashi really did carry himself with a lot of self-confidence and strenght, always giving that prodigy vibes. So Rin being a kid didn't realize how young Kakashi actually is.
This changes after the Kannabi bridge mission. Kakashi, whose body is still adapting to his Sharingan, is unable to keep the confident facade due to the inmense pain he's in (I can expand on this in another post if you'd like), so he looks extremely vulnerable and small.
After seeing Kakashi in this state, Rin can't ignore anymore that Kakashi is a kid even younger than herself and inmediately drops her crush.
So now Rin sees Kakashi as more like a little brother, and she decides to look after him. (This comes from what little caracterization we have in canon of her. In the scene where Obito dies, while Kakashi is crying and shaking, Rin inmediately stops crying when Obito asks her to do the transplant, showing her incredible mental strength).
And she takes care of Kakashi not just because she understands how important he was to Obito, but also as a way to cope, in the same selfless (but unhealthy) way she's always known. She needs this, needs to take care of someone vulnerable to help herself. After all, she was really messed up by Konoha and the war, she is still a child soldier who got her obsession with being useful to the village drilled into her head. So she distracts herself from her own grief by helping Kakashi with his, thinking it's what Obito would have wanted, even if it's slowly destroying her.
Because here's the thing, Rin underestimates how important she truly was to Obito and prioritizes Kakashi over her, in the same way Kakashi prioritizes Rin. Neither realizes that both of them were the most important people to Obito.
So in summary, Rin seals her own pain and refuses to cry or show weakness in front of Kakashi (supporting him like she supported Obito) but at the same time she spends most of her time with him with the excuse that sheโs helping him with the pain from the Sharingan.
They sometimes sleep in the same hospital bed, hugging and exhausted, and then there can be heard soft sobs and sniffles. But it's impossible to know which one of them is making those noises.