When Olivia says these words to Sebastian, the emotion she is feeling at this moment is overwhelmed. She is overwhelmed with her love towards Sebastian.
Olivia is <em>overwhelmed</em>. At the moment she speaks these words to Sebastian, Olivia feels an <em>overwhelming emotion</em> (<em>that has such a great effect on you that</em> <em>you feel confused and do not know how to react.</em>), which is shown it the expression "breathless with love". Another indication is when she asks Sebastian "Plight me", meaning "promise me you will marry me."
