Ah, reciprocity. Remember to take care of your loved ones, even if they have the dreaded Corona Coof.
I don't think his mom expected that the instant he got sick he would have a girl come over. Or that he would ever have a girl come over.
Hell, I kinda find it sweet that she's returning the favor and that she's so concerned, but not so concerned as to drop the facade of teasing him.
Some details to notice:
-Page 7, bottom left hand corner, you can see her silhouette.
-The second her gets upset and starts having a coughing fit, she panics and stops looking for magazines because she's concerned about him
-Notice that Nagatoro kinda goes through the five stages of grief (Sans bargaining) when she realizes Senpai isn't at school. First she kinda teases him asking him if he's left the country and harassing him (like she's in denial), then she gets upset and yells at him when she realizes he's not in school and has the flu and didn't tell her, then she skips over bargaining and gets sad that she spread it to him. When she realizes he's okay, she goes back to tease him again and accepts it.
--Also note how she immediately gets concerned again when she realizes his parents aren't home, and goes silent
for once, drops the facade and immediately goes to his house.
-She doesn't even acknowledge the President as anything aside from "the Bunny Girl," and she says that she wrung it out of her. Not only does this indicate that she doesn't have much respect for the president (she sees her as a rival) but that she's probably both jealous of how she knew his address and he didn't and how she somehow was able to get it out of the President, meaning she was able to annoy the most stoic individual in this entire manga.