What ever it was, I am glad to say, the biting hasn't continued. The bites are very itchy at times and it wakes me up at night, but often I hardly have any itching.
Strangely, there are marks on my upper chest and neck that look like 2 and 3 inch scratches from claws, but they are also bites.
I also braved it out and picked up the same chicken, at arms length. (Both times it was daytime.) She didn't appear to have any mites, but I didn't get a magnifying glass.
She does have some feather lice; beige easily seen bugs crawling on the feathers, not near the skin. I never saw anything like that on me.
Is it possible that she got into chiggers, right before my son handed her to me, and they crawled onto me from there?