Seems to me Akira's pretty much someone who hasn't really known failure - she's so ridiculously overspecced that so far she's probably been able to achieve essentially anything she's set her sights on with enough effort. Not surprising that this has gone to her head a bit, really.
Then she abruptly slammed headfirst into something where all her awesomeness is completely irrelevant. Now she's trying to get her bearings way off the map, having to come to terms with the limits of her till now unassailable competence with due ramifications to her self-image while coping with unfamiliar and intense new passions.
Growing up is hard to do.
To her credit she promptly recognised her jealousy for what it is and did her best to suppress it, and her initial knee-jerk ire towards Mayuki at the time of the revelation (which no doubt involved a vague, obviously irrational feeling of betrayal) has already simmered down to mere pouty "okay fair enough the kid tries her hardest but I'm still better, hmph."
She may be as volatile as any somewhat self-absorbed teenager grappling with all the messy business of youth, but she's also a basically good person who can't hold unreasonable grudges.