It’s really possible. Scientists using MRIs have been able to show that when an outside observer is with someone in pain, similar neurons in the brain are activated in both people. This process has been called a mirror neuron/circuit system.
Somehow the mind, body (felt sensations), and emotions are all linked together. As you’ve noticed, the sensations are not exactly the same for both people.
Animals also have a biologic response to the suffering of others. Mammals such as rats and apes seem to mimic and imitate others in pain. Scientists think this may be a way to learn about danger from other members of the species.
Some people seem more empathetic than others. Researchers are trying to find out why this happens and how we may be able to use it to help treat those in pain more effectively.