"Have you ever experienced a brand-new feeling that welled up inside of your heart and filled you with indescribable pain?"
A quote from the English translation of Cowboy Bebop: The Movie. Two characters are discussing a sort of painful, melancholic longing, like love but perhaps a new feeling entirely.
The Portuguese word saudade seems close, but I am aware that it does not have an English counterpart.
Is there a word I haven't heard that fits this description?