Genasi, Tieflings and Aasimar have been used as a sort of catch-all for any plane-touched, not just those that are primarily, on Amia. For instance, there's Celadrin among the elves, which could be considered Elf Aasimar, if I recall rightly.
This wiki page has a list of some others: http://en.wikipedia.org/wiki/Planetouched
I've seen a Halfing Air Genasi, countless Elf (Insert Element) Genasi... I don't believe everyone necessarily likes it for various reasons, but I also don't believe it's particularly against rules as long as you're not going over the top with it.
In general, if it isn't a Fire/Air/Water/Earth Genasi or if it is a specific type of Celestial or Fiendish plane-touched (such as the more bizarre ones on that wiki list), you should make a request just to get it cleared. That's my advice anyway, speaking from experience.
As for your style question, the classic appearance of a typical Air Genasi (whatever that is...), especially on Amia, has tended to be pale blue skin with white hair. This isn't the only shape of them, however. The amount of elemental heritage varies between people, some manifesting more obvious traits, others more subtle. As you've probably already read other places, they tend to have wild and "wind-swept" looking hair; there's a few heads across the genders that could help to get that affect across, if you wanted. I would say, though, that much of your specific appearance quirks are simply going to need to be expressed in your bio.
