Hiromi came to live with Shin. He's not sure exactly why. She's the child of one of Shin's father's "associates".
Apparently, years ago, Shin's mom took Hiromi aside and told Hiromi that she and Shin were half-siblings (same father). Thus, Hiromi is the living proof of Shin's father's infidelity. Thus, Shin's mom hates Hiromi, and treats her like shit. (This happens a lot in real life. Look up "displaced aggression".) Shin's mom also hates Hiromi's mom, which is why all those pictures were cut up. Shin's mom was removing the head of Hiromi's mom.
Hiromi tells Shin that she is his younger half-sister, which opens the door for her to call him "Onii-chan", but she NEVER FUCKING DOES IT. Not yet anyway.