I think Aya just wants to fit in with Mitsuki's family and future and she's decided all on her own that she MUST learn English to do that. She wants to understand the lyrics. She picked English as her focus for university. The three people she really likes all can do it. This might be the first time she was trying for something she wants that much. It doesn't seem like they know exactly how bad she's feeling about it because she is having fun with Mitsuki otherwise.
It looks like Mitsuki is currently happy in the moment and thinking everything is great while Aya wants to be happy, but is mentally stuck in plans/scenarios as she's done in past chapters. Before she was focused on ways Mitsuki could stay with her and now that Mitsuki seems to be in a good place, cooler than ever even, she's decided she has to do this to stay with her because that's how she's wired to be.
Yeah. I mean, Joe is definitely moving to America at some point, she's probably assuming Mitsuki will go with him, and she feels like she has to be able to thrive there herself in order to stay with her. And for a girl her age, who has probably kind of undervalued academic studies up until this point, that's a lot of worry and stress to put on yourself.