Could this be Margaret Peterson Haddix's Escape from Memory? It was published in 2005 and has a cover much like you remember.
While playing around with hypnotism at a party, Kira remembers fleeing a war-torn country with her mother, speaking a language she can't identify. A few days later her mother disappears, and a woman who calls herself Kira's aunt Memory takes Kira to Crythe, a country that doesn't officially exist, in order to rescue her -- or so she says.
Kira soon learns that Aunt Memory is not what she seems, and Kira and her mother are both in terrible danger. There are memories locked in Kira's mind that could get her and her mother killed. But those memories are the only things that might save them...
One of the reviews mentions that part of Crythe's culture is memorizing things, and the implanted memories:
This book was different then anything I've read or heard of. It dived into something that usually isn't even thought about: Memory. Yes, there's some books that has memory in it but it's not the main thing; it's not the thing that drives some characters to do what they did, like it does in this book. The community of Crythe is based on that one thing. Memory is what drives everything that they do and what happens to them, everything. And since Crythe is so important to the story and memory is so important to Crythe, then memory is really important to the story. Plus that's what puts them all in danger in the first place. The fact that Kira has her parents memory in her mind and that's what Rona (first called Aunt Memory) wants so much that she will kill them all to get it. So memory, this thing that is rarly set on center stage in a book, is what drives the whole story and that's original!
I found this by searching for science fiction young adult book implanted memories aunt mother although that was not the first set of search terms I tried.