Theory

I'm fully convinced at this point that the throw up scene was in fact a red herring and was obviously thrown in at that timing to confuse us. Upon rereading with the additional context, I think it's possible it was a way to show that Guwon was likely dealing with the same bug the little kid got. As we know, adult colds can be rough even for us, but that same bug for a little kid with no medicine can be quite fatal. Supporting evidence; He mentions not being able to provide teach with meds and for him not to feel too bad, because that same rule applies to him even when he's sick. He also mentions he hasn't been feeling well, tired, etc.

The comment where he's praising himself-- I think he was just earnestly doing so, not maliciously. I don't think he was trying to imply he was manipulating teach with his looks. I think he was just literally off handedly saying "Damn, I'm sexy". He has a habit of doing so from the first few times we see him, when he gives teach shoes. I think it's a habit.

Unrelated to the throw up scene, I'm more worried that them swapping blood will prove to be a bigger deal down the line