This is the novelette Monarch by Piers Anthony. I read it in his fixup novel Prostho Plus. I don't think it has been anthologised so you either read it in the original magazine publication, Worlds of If, or in Prostho Plus.
What's keeping you from your grand tour of the universe? Are you afraid of being caught out in the vastness of space with a painful cavity and no one capable of fixing it? Well fear not--the galaxy is simply teeming with dentists!
For Dr. Dillingham, dentist of Earth, it was the shock of his life--captured by aliens, forced to fix a strange cavity in an even stranger mouth; then whisked off to deep space. But luckily for the good dentist, Dillingham discovered that he liked zooming about the galaxy, solving unprecedented problems and making new and decidedly different acquaintances. And when he was offered the chance to apply to the Galactic University of Dentistry as Earth's first (and only) applicant, Dillingham had a choice to make: go back to his safe little world of bored housewives and miles of braces, or make a mark for mankind among the teeth of the stars.
It was really no choice at all.
The scene you remember is when the dental hygienist Judy (not the dentist Dr. Dillingham - Judy was Dillingham's assistance on Earth) is treating the king on the butterfly planet Lepidop. The king keeps going back in time to improve his teeth, but the problem occurs when he tries to go take himself and Judy back to before the date of Judy's birth:
"I have had a taste of better health," the Monarch said, shaking his faintly orange wings. "It incites me to desire more. If twenty years did this, what might thirty do?"
That would be equivalent to sixty, by her scale. He would in effect be twenty—at the very prime of life. Of course, nothing short of a complete overhaul from the moment of conception on would provide him with absolutely perfect teeth, but—
"If I begin caring for my teeth in the flush of my youth, at the time I first emerged from the chrysalis, they will remain strong forever!" he cried.
She kept forgetting that the butterfly lifecycle differed from her own. Perhaps that was time enough.
"Come, my dear—take my hand."
She tried to stop herself, but his word compelled her just as though she were a butterfly subject. "Wait!" she cried, suddenly realizing what thirty years would mean to her. "I can't go back to—"
And the vertigo overcame her.
It was much worse than before. She felt as though she were being turned inside out through the mouth and dipped in lye. She felt, she fought, she expired, she emerged into—
Nightmare.
The choking crying bleeding miasma of extinction. Her arms were bound in mummy wrappings, her eyeballs were rotten. She screamed with the soundlessness of an anguished ghost. Maggots were feeding on her tongue, flames on her wings.
She had tried to go back to four years before she had been born.
But it was not her own demise she experienced. The Monarch was dead. His ancient husk of a body dangled from her hand when she stood, and when she tried to let go his desiccated appendage it fell apart.
Judy is sentenced to death for her part in the king's death. She is tied to the top of a tower and targeted by lasers: The death of a thousand lights! She is rescued by a robot that has sworn to protect Dr. Dillingham (how and why the robot is protecting Dr. Dillingham is another story).
Searching the site for the story I find it was asked about before in the question: Children's sci-fi collection - Alien orthodontist. In his answer to that question user14111 points out that the novelette can be read online at archive.org.
