Hmm, have you ever read anything about codependence? I hate to throw that word around loosely. (Also kind of hate to medicalize/dramatize something that can sometimes be a natural reaction in life), but it does sound similar to what you are describing... Specifically the trouble in pinpointing your own feelings and that others' feelings are so easily picked up on.
It can be a pattern that develops very early and I would theorize can lead to feeling like one is running on empty after lengthy, difficult relationships as I believe you have mentioned before in several posts. Sometimes it takes a long while to rebound from those relationships if others have drained us dry emotionally. (A process in which we can often be unconsciously complicit :/.) It's like needing to refill our internal reservoir before being able to feel again.
I would ease up on yourself if you are being hard on yourself/over-analyzing your reactions in relation to the person you are with too... that can get in the way of the flow of feelings. Having very feeling oriented conversations with someone or being bombarded with their feelings before you're ready can be a bit much. (Bleh!)
I also think doing yoga/running can help a person get in touch with their core again if you don't already do that.
Sorry, this is a shotgun spray of advice but perhaps something will stand out to you.