As pointed out by OP in a comment, this is Slayers (2011) by C.J. Hill, the first book in the Slayers series.
Dragons exist. They're ferocious. And they're smart: Before they were killed off by slayer-knights, they rendered a select group of eggs dormant, so their offspring would survive. Only a handful of people know about this, let alone believe it – these "Slayers" are descended from the original knights, and are now a diverse group of teens that includes Tori, a smart but spoiled senator's daughter who didn't sign up to save the world.
The dragon eggs have fallen into the wrong hands. The Slayers must work together to stop the eggs from hatching. They will fight; they will fall in love. But will they survive?
This person was having a very vivid dream about a terrifying dragon that was trying to get to the person in the dream.
Mrs. Harriet Davis had never been afraid of dragons— until now. The dragon in her dream hovered above Washington, D.C., watching traffic. Against the fading light of the evening, its body seemed first brown, then maroon, then the color of blood. The dragon turned its head side to side, presenting a face that looked like a cross between a crocodile and a cat, although with more disdain than a cat and less patience than a crocodile.
At the end of the dream, the dragon either succeeds in catching this person or it just scratches them.
After the dragon lunges towards Harriet and breathes fire, the citizens she grouped with think it's gone, but that's when the dragon attempts to land a final blow.
“Is it gone?” a man beside her asked. Before she could answer, a searing hot claw grabbed her shoulder from behind.
It's at that moment when the person wakes up and they find scratches on themselves.
The following scene confirms both that, and the "it might have been a girl and I'm pretty sure she was pregnant" part:
Harriet gasped, let out a strangled scream, and found herself sitting up in bed.
Allen threw off his covers and turned on the lamp on their night-stand. His blue eyes
were wide, but not quite awake as he jolted out of the bed. “What is it? Is the baby coming?”
She shook her head and drew her knees up, trembling, gasping. “A dragon grabbed me! Its claws burned into my back!”
Allen stared at her a moment, then laid back down with a thump and shut his eyes. “Okay, let me know when it’s the baby.”
“My shoulder burns like crazy.” She slid her nightgown away from her skin and gasped. Three long welts ran across her shoulder and down her back. “Look!” she cried. It was proof she would rather have not found. A wave of nausea swept over her.
Allen sat up, squinting at the welts. “How did you get those?”
Her voice spiraled upward. “I told you. It grabbed me.”
This person and her husband(?) proceed to call someone who is of the right expertise to help them.
When she was dreaming, Harriet remembered a scientist on the radio, talking about how dragons were real. She hadn't listened to what followed, thinking it was not serious, but after the dream she had, she and her husband reached for Dr. Alastair Bartholomew, who spent his life studying dragons. He tells them about how their child is going to be one of the new generation of Slayers, and that is why the dragon tried to kill him in the womb.
All quotes are from the book's prologue, which can be read (along with the first 35 pages) on the editor's website.