Just gonna go against the grain here and say that:
a) I hate this side "couple" and
b) the nurse saying "hurry up and graduate" made me wanna puke. It's almost no different from when people used to have countdowns for when some famous underage girl was gonna turn 18 in the 90s (eg Emma Watson). Yuck.
Shit like this creeps me out and then the comments calling it 'cute' creep me out even more. Y'all give way too much of a pass to things just cause it's two female characters instead of a grown man and an underage girl (which brings up another problem: fetishization of lesbian relationships, treating them all as inherently 'pure' and so on).
I'm glad this is being kept mostly to extra chapters instead of the main story or I would instantly drop this.
This argument assumes that all age-gap romances are inherently bad and exploitative. I've known more than a few such relationships in real life, cutting all different directions--younger man/older woman het, gay male, lesbian, etc., many of which have worked out long term to the satisfaction of both parties (and some that didn't, like other relationships). (Note: I'm not talking about student-teacher relationships below the graduate-school level here.)
And in this particular case, it's not even clear that the nurse is saying, "Hurry up and graduate so we can be together." Granting for the sake of argument that she is attracted to the student, she could mean, "Hurry up and get on with your life away from here so I won't be tempted into something inappropriate." Whatever she feels, she hasn't done anything wrong.
So be creeped out all that your heart desires, but don't assume that you're voicing a universally applicable moral judgement.