Did those 3 last panels implied that she is the one who caused the accident or am I overthinking it?
I don't think so. I think it's supposed imply that the onee-chan realized that even with amnesia, her sister is still in love with her and that she herself still wants the relationship (hence the "Don't call me Onee-chan, call me by name")
I was confused until the end note since I only read a bit of the first Harry Potter book. I still don't understand how telling Ayumu about her Patronus would burden her though