I actually disagree with the MBTI test as well, too much room for failure. There is also a huge difference between acting like a personality type and actually being one, the test cannot make these distinctions like a person can.
So you are essentially feeling empathy for people?
Let's clarify some things: When you see these people make these emotional responses, what is your face doing? Will you actually feel your own face responding, or are you just feeling what it is they are feeling on the inside?
So far it sounds like it is Fe.
Fe is a directive emotional function, this means that it is meant to influence the outside world in some way. It has two uses: To move people, and to read people. The way it moves people will come out in your voices' pitch inflections and amplitude, smiles, eyebrow raises, grimaces, even laughs.
For example every now and then I will say something that I fear came out too cold, so I will subconsciously throw on a smile at the end of the sentence so the other person knows to feel that what I said is not as serious as it sounds. When Fe reads people's then it is usually to recalibrate how it is going to send out it's own. This last part commonly display itself as the INTP's "Social chamenleon" tendencies. We read the other person's emotional content, and then match it with our own.
Basically it is emotion meant for the direction of the other person.
So based on the fact that it sounds like you are reading the other person's emotions and them matching them, it sounds like Fe. However, Fi can be very empathetic as well, but for an Fi user, the emotion is meant for themselves, and is not for the benefit of the outside world. Very much in the same way that Ti is meant to be our own way of understanding things.