Since it has been brought up so far, I figured I'd toss my opinion into the labels discussion. In general 'alex' and 'feeler' aren't derogitory and are simply meant to me shorthand. The big caveat is that they shouldn't be used or applied to someone unless they are ok with it. Some people that act like alexes may not be or may be resistant to the idea that they are different or that they have alexithymia. I would've said that the first thing to do is to share the information with your SO to see if they are interested in learning more and see if they do have alex. I say would've because it seems you have already done this.
If you are both new to this, it is a good idea to read up on it as much as you can. A good book for general overview/introduction is Emotionally Dumb (
http://www.amazon.com/Emotionally-Dumb-An-Overview-Alexithymia-ebook/dp/B0038VZJ9U). Hopefully, as the two of you read up on it, she will be able to identify how she handles things and the best way you can help communicate.
This may or may not apply: when describing your emotions, try to use more basic words (already said) and try to express the reason for your feelings. Even if someone can't put a name to the nuance of feelings, understanding the context of the feeling can clarify what "angry" or "sad" mean.
This also may not apply: Emotions help people to read, process, and act in new situations quickly all subconsciously. Since alexes can't do that, they must read and process new situations consciously, which is harder and slower. For me, this means that trying new situations or being around new groups of people takes a lot out of me and can be very daunting. It may be that there are things she keeps going back to doing (recharging) and things she is hesitant to do (outside the bubble).
Ultimately, working together to understand what alex means to her will give you the best idea of how you can be there for her. As for you (and all other SOs of alexes), make sure you have a support group outside this relationship. Alexes bring a lot to the relationship, but generally struggle with contributing emotionally to the relationship. Spending time with family and friends that you can emotionally interact with normally will allow you to meet that need for you so that your SO doesn't need to.
Hope this helps.