"Unwillingly to School", a novelette by Pauline Ashwell; first published in Astounding Science Fiction, January 1958, available at the Internet Archive; reprinted in the anthology Uncollected Stars and in the Pauline Ashwell collection Unwillingly to Earth. [P.S. Scroll down for update.]
Beginning of the story, the narrator/heroine introduces herself:
This may look like a moviegram of Brownian Movement but no such luck; it is Russett Interplanetary College of Humanities Opening Day, four thousand three hundred twenty-seven other freshers milling around and me in the middle with a little ticket on my chest says Lee, L. because my given name is something not to mention; they say these kids came from one hundred twenty-four planets just to study at Russett but personally of all points in the known continuum this is the one I would rather be any place But.
Freshers come in all sizes, all colors but a fair number are girls so there is one thing we will be finding in common anyway.
This may come as a surprise, that I am a girl, I mean. My tutor at Prelim School says my speech is feminine as spoken but written down looks like the kind of male character who spits sideways.
I reply that I talk like my Dad he is a character all right, male too but does not spit, if you spent your formative years with a filter in your kisser neither would you.
He says my flair for seeing the functional significance of the minutiae of behavior is obviously what got me chosen for the Cultural Engineering course.
I know what got me into that all right I am not so dumb as I look.
Her trouble with reading machines:
Beschrievene says that the safety device only turns off the Crammer, the rest of the machine goes on working but only at the rate for unassisted reading about one-tenth normal rate.
M'Clare says, "You, my girl, have been trying to keep up with a course designed for people who could absorb information seven or eight times as fast. No wonder your knowledge seemed a bit sketchy."
The story continues with "The Lost Kafoozalum" in Analog Science Fact & Fiction, October 1960, which was reprinted along with "Unwillingly to School" in Ashwell's collection Unwillingly to Earth, and is available at Project Gutenberg.
I'm not sure if Professor M'Clare is the head of the school, but she does end up marrying him:
"You know, Lizzie, I dislike risking the lives of any of the students for whom I am responsible, but as it happens I find the idea of you—blowing yourself to atoms particularly objectionable because ... I happen to be in love with you. You're also one of my best students, I used to think that ... was why I'd been so insistent on your coming to Russett, but I rather think ... my motives were mixed even then. I meant to tell you this after you graduated, and to ask you to marry me, not that ... I thought you would, I know quite well ... you never quite forgave me, but I don't-want-to-have to remember ... I didn't ... have the guts to—"
[. . . .]
It is just as well my Education has come to an honorable end, because ... well, shades of ... well, Goodness gracious and likewise Dear me, I am going to marry a Professor.
Update. Actually there were four stories in the series: the two I mentioned and two more published decades later. Quoting Wikipedia (some links added):
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.]