Having empathy has nothing to do with being or not being an empath. Some empaths are very empathetic, and most empathetic people are not empaths.
True, I'm an Empath, for sure, and I can be a b*t$h. But if I stay grounded and try keeping my vibration high, then I'm tolerable. Lol. Empaths do not just feel others emotions but can actually roll play them without realizing they are acting out someone else's emotions. I also feel physical pains of others. ...then some days ....I may just be in a bad mood. After I started gaining somewhat control over others emotions, I could tell the difference in who's emotions I was feeling , mine or someone else's. Empaths have bad days to. Just because we have this gift does not mean we are the nicest people on earth. We have our limits just like every one else.