They sound like lice, rather than mites (yes, I'm itching now too

)
You can get Frontline spray from the vets, that is effective. You need to reduce the dosage depending on the weight of the bird - for example, if it's 6 sprays for a cat, then it might be 2-3 for a chicken, depending on size.
As MS says, the environment needs treating - diatomaceous earth, Total mite spray.......