Welcome to BYC! Good luck with your little chick 

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I don't see anything stuck.Welcome to BYC. Have you checked inside her mouth, to make sure she doesn't have something stuck?
They are supposed to be easter eggs but considering we have gotten "barred rocks" that turned out to be we think Australorps from the same place. Not complaining to much since we got a beautiful and actually very friendlyYou might Google "brooder pneumonia" and see if she has any of the symptoms.
BTW, I think they may be crested cream legbars, not easter eggers. They are blue egg layers too.
I've had 2 legbars, from seperate purchases, that have failed to thrive, and remained very tiny. One died at around one year old, she never layed eggs. The other is alive, and seems well. Though at 17 months, she has never layed an egg. She is bantam sized.
I am currently reading about dwarfism in chickens. I've read that dwarfed chickens, often have a short tongue which can cause choking when they eat. I wonder if that might be the problem with yours.
In any case, I want to wish you and your chick, the best.
They are supposed to be easter eggs but considering we have gotten "barred rocks" that turned out to be we think Australorps from the same place. Not complaining to much since we got a beautiful and actually very friendly
rooster that's been with us for about 4 years now. They do seem to have markings like a Legbar as well though after looking! So major possibility.
It's possible that they could be a legbar cross, which would be an easter egger.I did also read this from the hatchery that tractor supply uses. So that could also be why they favor legbars. Due to being a crossbred