I think people confuse empathy and sympathy. Not even sure if empathy even exists.
If I stub my toe, other people can sympathize with my pain, but I am the only person feeling it. Pain is not telepathically transmitted to those around me.
But, gosh, I'll bet other people have stubbed their toe before as well and have also suffered similar pain that they can then recall and thus empathize with you.
Still more have had pain that produced a reaction similar to yours and that allows empathy as well.
Gosh darn, we can empathize with each other after all.