A quick story walkthrough and event synopsis of Asylum: chapter three:

This is a bit late so I’m going to try to take back up the slack but these take a lot of time and effort so we’ll see.

-The chapter opens right where the last left off, with Twilight starring at AJ while her mind is once again fogged by “The thick strands of discordant thought gumming up the works of her brain until it felt as though it had stalled.“
-Twilight doubts the authenticity of the pony standing before her, considering her “an existential threat to her memories given life,” and as she introduces herself Twilight’s mind is filled with an “opera hall beset by a bellicose chorus,” and her mind begins to race through many possible explanations including Changelings, Discord, a magical curse and everyone being brainwashed.
-Twilight is snapped out of her thoughts by AJ, who is happy when Twilight recognizes her.
-Aj says it would be a good idea for Twilight to ask her some questions, as it might help with the amnesia, and all Twilight con come up with is “Where’s your hat?”.
-After AJ tells Twi that she doesn’t were her hat while on duty Twi asks when she became a doctor and AJ responds that she graduated from Manehattan School of Medicine ,” two years ago.
-Twilight begins to ask about the farm and Big Mac but when she asks why AJ when to medical school and he did not AJ gets angry and shouts that he is not.
-AJ apologizes to Twi as if to a child and Dreamer suggests that instead of letting Twi ask questions Aj should just give Twi her whole life story.
-AJ says that her parents always wanted their children to get a good education and go in to a prestigious field but while Big Mac was in Canterlot University her father contracted cancer and became bed ridden with her mother doing most of the work and only allowing him to do small jobs on the weekends.
-After some time her father dies and her mother shuts down mentally,causing Big Mac to drop out of university to pick up the slack at home.
-AJ says that as she got older BM insisted that she keep in school and wouldn’t let her skip out for anything, something she came to resent him for but later realized he had sacrificed his own future for the family.”
-After AJ graduated hight school she decided to go in to medicine and applied to Manehattan School of Medicine because she could get free room and board from the Oranges, since she could not afford it otherwise.
-She states that university life was hard and that for many medical fields “magical ability is an unspoken prerequisite” and that even where it wasn’t non-unicorns would still be discriminated against.
-After she graduated she decided to work at Broadhoof because it is where her mother spent her last years and because it is close to Sweet Apple Acres.
-AJ explains that when she arrived her job was to accompany patients while they got their exercise and that her first assigned patient was Twilight.
-Aj goes on to say that since Twi was silent she would talk to her about everything she did not have anyone else to tell.
-A month after her arrival AJ is placed in charge of a bi-weekly therapy group including Fluttershy, who would sit away from the group.
-Dreamer referees to Flutters as “bargirl” and AJ chastises him for it. This is apparently a reputation she has.
-In an effort to have the patients open up a show&tell is implemented but when it si Fluttershy’s turn the bird she shows is killed, causing her to attempt suicide with one of the small birdcage mirrors in her room, for which AJ blames herself.
-Aj says that after that, when she had a few days off and was absent form the walks she usually took with Twilight, Twilight asked about her and seemed upset when she learned that AJ wasn’t coming. Then Twi produced a craft she made.
-Back in the present AJ takes out the craft with is a folding piece of purple origami with the message “Hope everything gets easier for you soon! Your friend, Twilight Sparkle.”
-Twi checks and then affirms that it is in her hand writing and then gives it back.
-Twilight analyzes the pony infant of her and comes to the conclusion that this is the same AJ she knows and tells her that they are still friends.

Short version:
Twi sees AJ, they talk about AJ’s past and bring up Flutters for the first time and Twi accepts AJ as her friend.