Well there are a lot of things that make me think you are emotionally aware. For one thing in your OP you seem to notice the behavior of your parents a lot. You also have a sense for what the healthy outcome in the situation should be. Not everyone picks up on those kinds of things. Sometimes people know that something is wrong, and it bothers them, but they aren't sure what would make it better or what would be healthier.

I also looked at your posting history a little. You seem very bothered by how people treat each other. To me that suggest that you are sensitive and paying attention to how things unfold socially. You also asked a questions about black and white thinking and in one of your posts you mention how extremes can be important and how gray can be its own extreme. This suggests you are able to think about emotional concepts in a complex way, and tend to evaluate things a lot.

Another thing you have mentioned is that you are socially anxious. Often times people who have social anxiety are emotionally perceptive people. The problem however is that they spend so much time reading social situations and thinking about all of the things that could go wrong that they get overwhelmed and decided not to engage at all. The good news though is that a sense of that kind of thing can also help you know what the right thing to do is. But taking the risk and finding out if you can succeed might feel like too much for you right now because you are struggling with your self confidence (but that is something that can get better with good therapy).

I think that you might be the kind of person who is more aware of how others feel than how you yourself feel. Not an uncommon problem, really. That kind of thing can stem from living in a situation where you are expected to be aware of how other people are feeling all the time, but no one reflects back to you the way that you are feeling. A therapist who can reflect back to you how you are feeling and who notices who you are as a person might be very important for you.