Do they though? Is not the experience of an emotion the realization (or concern) of that emotion?
I don't think so. We're constantly receiving sensations towards which we are inattentive. This is particularly true for emotions. People don't always recognise their own feelings and inducements; very often, the thoughts and ideas that are conspicuous within our minds, are pervaded by a sort of undercurrent of feelings of which we are scarcely aware. You could imagine it like being in the presence of conversation that you aren't appropriately listening to. You're probably perceptive of same vague feeling that corresponds to sound, but besides that, you can't determine what the speakers are discussing. You're experiencing something that you're ignorant of. So, no, experience is far removed from concern.
This is very interesting, I don't know that I've ever thought of emotion in this way. I suppose I've always just thought that the emotions I'm fully aware of experiencing at a specific moment are the only ones I'm feeling at that moment. But what you're saying is that like on a smart phone, there are "background emotions," if you will, that run even without us being fully aware of them. This definitely explains why a person could feel anxious, and have not a single clue as to why.