Dwan was born in Coosan, Athlone, County Westmeath, Ireland, and originally trained as a ballet dancer.

Dwan's first movie was playing the role of Agnes in an adaptation of Oliver Twist, co-starring Elijah Wood and Richard Dreyfuss.

Dwan performed the piece again in July 2009 at the Southbank Centre in London in a time of nine minutes and fifty seconds, and again at the International Beckett Festival in 2012.

[9] Beginning in 2013, Dwan toured with "The Beckett Trilogy", consisting of Not I alongside two of Beckett's other short plays, Footfalls and Rockaby, under the direction of Walter Asmus at the Royal Court Theatre, West End, The Barbican Centre, and the Brooklyn Academy of Music, and performed sold-out shows at various international locations.

[15][16][17][18][19][20][21] In 2021, Dwan played Tori Matthews opposite James Nesbitt in Bloodlands, an acclaimed four-part BBC drama.

[26] Dwan was also a 2017–2018 artist in residence at Columbia University, where she worked with Irish writer Colm Toibin on Pale Sister, a play derived from the class they taught called "The Antigone Project".