Empath is a pop-culture term for characgers in fiction with a heightened spiritual ability or something.
The first problem i see is attributing that term to a real condition of someone having hyperempathy. People with hyperempathy are very in tune with the apparent feelings of others, maybe to the point they over-read the feelings of others. Tense situations with people are especially difficult. Perhaps using the same term for both affects the way one would interpret their condition as an overly empathetic person: "because thats how empaths are in fiction, this must be how I should interpet what it is I sense from other people," one with hyperempathy may think, and before they know it, they're seeing what they want to see, feeling what the want to feel, all in order to validate a fictional definition of a condition they have. But hyperempaths in real life dont have supernatural powers; it'd be easy to interpret that way because the more empathetic you are the more easily influenced you are by external ideas.
Reskew, if you have heightened empathy, I believe you, and I do as well, but you probably shouldn't be surprised if people dont take it seriously when the definition you use for it is the one used in science fiction, and likening it to a superpower.