Swallow was raised in Jacksonville, Florida. While at Stanton College Preparatory School she began acting in various college, amateur and professional theatre productions. She graduated in 2001 with a BA in Middle Eastern Studies from the University of Virginia, and then studied for a MFA in Acting from New York University’s Tisch School of the Arts.

Swallow continues to act on stage whenever she can, starring in world premieres of Donald Margulies' play The Country House at Los Angeles' Geffen Playhouse, opposite Mark Rylance in Louis Jenkins' play Nice Fish at the Guthrie Theatre, and in John Patrick Shanley's musical Romantic Poetry at Manhattan Theater Club. She is not tethered to any one genre and jumps from Shakespeare to musicals to contemporary comedy in shows on Broadway, Off-Broadway, and in LA and Minneapolis. She won the Falstaff Award for best Female Performer in 2010 for her performance as Kate in The Taming of the Shrew.

In 2012, Swallow and fellow singer/comedian Jac Huberman created a stage show called Jac N Swallow, which they perform in New York at the Laurie Beeckman Theater and Joe's Pub. The show centers on the comic misadventures of the duo as they navigate very different life challenges with varying degrees of sanity and dignity. They are developing a series based on the characters.

In 2013, Swallow took her first role in movies, in a yet-to-be-titled thriller directed by Shana Betz scheduled for release in 2014.

Swallow's first television role was in Guiding Light, and she later played parts in Southland, Ringer, The Good Wife, NCIS, Flight of the Conchords, Medium, as series regular Dr. Michelle Robidaux on TNT's medical drama Monday Mornings and Rizzoli & Isles. She had a starring role in The Mentalist as FBI agent Kim Fischer. In 2015 she was cast in the eleventh season of Supernatural as the new character Amara, "the Darkness".