Empathy is first and foremost psychological. Yes, empathy can be used to process spiritual information, but so can hearing and sight. That doesn't mean we need to pluck out our eyes or deafen ourselves because it has that ability. Everyone is empathic, but some are more aware of it than others. They are generally more "in touch" with their emotional side. To go back on this is actually unhealthy. People that shut down their emotional side and are not empathic are straining themselves mentally. When empathy runs your life, that means your emotions run you. And that's bad. You need to learn how to observe and let go of your emotions as they come. You can use any form of self help or even real counseling to deal with this. But understand it isn't something spiritual to shut off, but something psychological to face and learn to control. It will make you a stronger, more balanced person.
Do research. It is technically a neurosis, so you are right about the illness part. If you are not in control of your emotions, you do not have good mental health.