I can feel empathy in the way you talk about, for sure. Sometimes it's not intense in person though (although I would still help if needed). Sometimes the more intense stuff comes when I'm just thinking alone later on. As for sharing typical emotions though, no. It's almost like... that scares me in a way.
Like, there's that question on the cognitive test here that asks "Do you feel intimate oneness with people?" and I put it pretty low. That's a unique occassion that I'd reserve for love/closest friends/family/or that deeper empathy I mentioned above, usually as a result of some trouble they're going through.
Negative emotions definitely have me wanting to get out. Or if I detect massive ignorance or (not to be extreme) darkness, I need to leave.