That is the basic trait of being an Empath. We feel people's emotions and because we are so empathic, we can heal them emotionally, too. It is built in to your being, kinda like breathing.
All my grandkids are also Empaths, though sometimes I think that they believe that I am out-to-lunch. When I have talked to them about being an Empath, they patronize me, but I can tell that I'm not getting through. Imagine my surprise when last week my 18-year old grandson texted me after attending a funeral of a classmate. "You are right. I am definitely an Empath and funerals and Empaths don't mix very well at all!" He had felt everyone's sadness and it was driving him crazy.
Why am I telling you this? Because now that you know what you are, you can take steps to prevent total burnout. At the top of this website page, there is a link to the Empath Survival Program. Read it and master your emotions before life becomes overwhelming. There is lots to learn, but shielding is a basic that all Empaths need to learn.
Sending you good tidings and best wishes.