People from other countries aren't going to bother to know the difference between an indianian and a wyomingese unless you bother to learn the identities of India. Everyone knows American = from USA because it's been spread like this for so long. American can also mean people from the continent, and the context of that is usually pretty clear.. What else would you say anyway? United Statesian? That sounds dumb. Mexico's official name is the United Mexican States, and no one calls them the United Mexican Statesians, they just say Mexican. Even though they have states just like the US.
Feeling pride in your state is great, but to anyone outside, it doesn't really mean much in the way of what to call you. You're still an American. Just one who likes where they live in comparison to a place they don't.