Well, in ch.3 it was "Classmate", but there was also shown that they spend decent ammount of time at school together, so who knows.
(Or maybe it was author wanted to reveal that kind of information out of the blue in this chaper... We will never know)
Well, like one popular song says, "It starts with one...". The more people know (especially outsiders), the harder it is to keep a secret, plus there is no guarantee that Maebashi would keep it a secret...
Beside, she knows he has a fever, so even if he sent that, it would fall into "he's fever got so bad he is not thinking sttaight" category, no?
Besides i think about did that so he could later stengthen theit love for each other... maybe...