Yes. That is the simple answer. The more complicated answer is yes, everyone is an empath to some degree, whether or not they recognize it, understand it, like it or dislike it. Empathy is a spiritual, metaphysical gift. As with any gift, it can be misunderstood and misused.
There are many degrees of empathy. Everyone has some sense of emotions and physical pain in others. Even the most callous and uncaring person has some empathy. Those people are just adept at hiding it away beneath their own negative emotions. The people who most commonly refer to themselves as empaths, are those who are highly sensitive to emotions and/or pain from others but have difficulty not taking those emotions and pains into themselves.
I am a highly sensitive empath, with the ability to sense emotional energy of others. I have learned to block the negative emotional energy of others from being taken into myself, while sharing my own positive energy with those who are open to it.
Being an empath should not be used as an excuse to mistreat others in any way, become an introvert or escape with alcohol and other chemical substances. Those paths only lead to more spiritual darkness and human self loathing. If you view your empathy as a curse, you have not truly discovered the spiritual nature of your gift.
Use all the information and tools at your disposal to learn about your empathy. Find out who and what triggers the negative feelings and why you are allowing them into yourself. Identify which feelings and emotions are of your true self and which are not. Set your intentions to block out all negative energy, emotions and pain from people around you. Your spirit guides are listening. They want to help guide you to a fulfilling and peaceful existence. You must believe in your own ability to identify and separate your own emotional energy from others. Your spirit guides know what you believe and they know when you have convinced yourself of those beliefs. Trust your gift, believe in yourself and you will be able to share that gift. The best gifts are those shared with others and it is always more fulfilling to give than to receive.