I've seen this term "empath" be used by people who are often coming from unique circumstances, usually having been abused in some way in the past. This is a person who doesn't know how to speak up and set boundaries and, as a result of this, will "take on" the emotions and problems of others as a survival technique. This was my own personal experience as well. Once I started to take ownership of my own feelings, sure, I was able to have space for other people's feelings but they did not impact me in the same way because I was no longer depending on the emotional state of others for my sense of happiness, fulfillment or survival.
The ability to have empathy for human is normal... Everyone experiences. It's not unique or special and if you think you're experiencing it in a unique or special way most likely it's a trauma survival technique and has nothing to do with you actually caring more about other people... Only that you are afraid of what would happen if you expressed boundaries and stopped enabling others.