I have often interpreted the 3 of Swords as representing a lack of communication, which can either result from or lead to heartache. Another possible meaning is heartbreak, particularly when a third person ("the other woman/man") is involved. It can convey feelings of being left out, self-pity, jealousy, or envy.
Allow me to share two personal examples that might provide further insight:
On a particular morning, I drew the 3 of Swords as my card for the day, alongside the 9 of Swords and 10 of Swords. I was grappling with issues in my best friendship, feeling jealous of the time my friend spent with his new girlfriend. I experienced a sense of being left out and lonely but couldn't communicate my feelings, knowing they were unreasonable. This lack of communication led to an argument, and I later discovered he had kept important health concerns from me, leaving me feeling betrayed. Although we eventually resolved our differences, it was a true 3 of Swords moment for me: jealousy, isolation, heartache, and betrayal.
Following my breakup, I consistently drew the 3 of Swords. I was in denial about my grief, and the card encouraged me to acknowledge my broken heart as a necessary step toward healing.
I hope these examples provide some clarity!💝