You may be thinking of Pauline Ashwell's 1992 collection/fix-up novel Unwillingly to Earth, described as follows on her Wikipedia page:
Unwillingly to Earth (1993), a fix-up of four previously published stories detailing the space adventures of the young Lysistrata (aka "Lizzie") Lee, including
"Unwillingly to School" (Astounding Science Fiction, January 1958), set on the rough mining planet where Lizzie was born and from which she was sent against her will to university on Earth. [Available at the Internet Archive.]
"Rats in the Moon" (Analog Science Fiction/Science Fact, November 1982), where Lizzie exposes plots of interplanetary political corruption on Earth's Moon.
"Fatal Statistics" (Analog Science Fiction/Science Fact, July 1988), where Lizzie negotiates between hostile factions on the planet Figueroa, whose civilization collapsed, and helps survivors make a new start.
"The Lost Kafoozalum" (Analog Science Fact -> Fiction, October 1960), where Lizzie takes part in a daring plot to avert nuclear war on the planet Incognita, and when things go terribly wrong she sets them right, saves the life of her professor and eventually marries him. [Available at Project Gutenberg.]
I've only read the first story, "Unwillingly to School", which was the answer to this question. The professor is Dr. D. J. M'Clare, Professor of Cultural Engineering at the Russett Interplanetary College of Humanities, on Earth; he finds Liz on her rough mining planet and takes her back to Earth to study at his school. As Liz tells it:
Where I grew up is Excenus 23, how I got hauled off it is due to a string of catastrophes but the name of the biggest is D. J. M'Clare.
Excenus sun is what they call a swarmer, ninety-seven small planets in close orbits plus odd chunks too many to count. Twenty-three is the biggest, gravitation one point oh seven Earth diameter is a fraction less, if you ever heard of the place it was because they mine areopagite there. Ninety-four percent production for sale in the known volume of space comes from mines on Twenty-three; but for that, no reason to live there at all.
My Dad started as a miner and made his pile, then he took up farming and spent the lot, he has it all back again now.
Liz doesn't want to go but her Dad convinces her:`
[. . .] and he says Going to send you to College, girl.
I say What!
Dad says Liz, Excenus is no place for a young girl all her life. Time you seen some other worlds and I cannot leave the farm and got no one to have an eye to you, now M'Clare says he will get you into this College and that is just what I need.
I say But—!
Dad says They got schools on Earth for kids like you, been on an outback planet or education restricted other ways, they are called Prelim Schools; well you got the Rudiments already; M'Clare says after three months Prelim you should be fit to get into Russett College of Humanities, he will act as your official guardian while on Earth. Do not argue with me Liz!
As first-person narrator Liz does not talk about her own accent (in the parts I've read) but no doubt she has an outplanet accent:
Each person says a name and the monitor repeats it to the kind of box he carries and this lights up with figures on it. I wonder why the box needs a human along and then I remember, one hundred twenty-four different planets and accents to match. I guess this is one point where Man can be a real help to Machine.