I usually read the 3 of Swords as a breakdown in communication, which can either come from or cause heartache. It also often points to heartbreak when a third person is involved, the classic other woman/man scenario. I also see it in feelings of being left out, self-pity, jealousy, or envy.
Two personal examples that might make this clearer:
One morning I pulled the 3 of Swords as my daily card alongside the 9 and 10 of Swords. I was struggling with my best friend because I was jealous of how much time he spent with his new girlfriend. I felt excluded and lonely but didn’t say anything because I knew my feelings weren’t entirely fair. That silence blew up into an argument, and then I found out he’d been hiding a serious health issue from me. I felt betrayed. We worked it out later, but that whole period was pure 3 of Swords energy: jealousy, isolation, hurt, betrayal.
After my breakup I kept pulling the 3 of Swords. I was denying my grief, and the card basically forced me to admit the heartache so I could start healing.
Hope these examples help clarify things! 💝