Cosm, a 1998 novel by Gregory Benford. is at least a partial match. As I recall, the main character is a black woman physicist, working at a collider, who accidentally creates a universe, sneaks it out of the lab and takes it home with her. I don't recall the part about her making more universes, but then I don't think I read the whole book. I'll see if I can find my copy or else some reviews or something, and maybe add to this answer.
P.S. I found my copy. From the back cover blurb:
After an accident in a brilliant young physicist's most ambitious experiment, it appears: a wondrous sphere the size of a basketball, made of nothing known to science. Before long, it will be clear that this object has opened a vista on an entirely different universe, a newborn cosmos whose existence will rock this world and test one woman to the limit: the physicist who has ignited this throilling adventure.
The brilliant young physicist is a black woman named Alicia:
A cool breeze whipping by reminded her that spring was still laced with chilly air skating down from Canada. The gust unfurled her bun and sent tendrils playing about her face. She felt she must look even more peculiar than usual, a big black woman with the classic African bulging bust and rear, a blob bobbling along on a spindly bike. Definitely out of place on Long Island. She had never entertained the slightest hope of resembling the willowy models of Vogue; those she regarded as aliens from another world, whom all true human females hated.
She zoomed on her beat-up bike alongside an enormous grassy berm, nearly four kilometers around and buried in the sand and stone of Long Island. Slanting morning beams highlighted the immense curve of the Relativistic Heavy Ion Collider, a giant swollen wrinkle. She had used the acronym RHIC, pronouncing it Rick, for so long that she thought of it as somehow male. Taking in deep breaths, she coasted amid pine trees just showing the light green tips of new growth.
And here, near the end of the book, some talk about other "Cosms" with different physical constants:
She chuckled. "What we just saw wasn't big enough?"
"Granted. I mean, conceptually. Look, do you think the production of Cosms will stop here?"
She thought about Brookhaven, about the sociology of particle physics, of the personalities, of the entire horizon-pushing history of the cultures that had come out of Europe over five hundred years before. "No."
"And the Brookhaven Cosm, it's not quite like ours. It differs slightly in some fundamental parameter, apparently, though we don't know which one yet."
"So?" Lazy warmth, the buzzing slowly getting louder, then fainter, then louder again: a search pattern.
"Any future Cosms we meddlers make can also differ slightly in fundamental numbers. Some will be changes that make life impossible, some will be good for life. Maybe even better than this universe, though ours certainly looks very finely tuned to make life possible."
