Who is Araragi supposed to look like in this scene?
This could possibly be a reference to the very obscure series The Soul Taker. The main character, Kyousuke Date, cried blood in few episodes. Here's a picture of him:



It's not an exact match, but Akiyuki Shinbo, the director of The Soul Taker, also worked on the Monogatari series, which made me think of this. (Source.)