Mites also invade a chicken that's health is compromised. If her beak was interfering with eating, that would compromise her health, lessening her general self care, bringing on infestations.
You will of course have to treat the whole flock, but I find it is those that are compromised that generally are the most infected, and can act like vectors to the flock. Since it may have been a long beak preventing good nutrition, I have every hope this hen will recover. See if that is the root cause; otherwise, it is probably something internal that is not fixable without mucho dollars from a vet. (At that point, I simply cull).
You'll need to treat the coop too. Use permethrin spray like Gordon's in the coop (after cleaning, spraying corners) and on the birds. Just in case it was your plan, DE does not work against mites. It is a nice thought but truly ineffective.
Good luck with her. Give us an update as to how she is doing after treatment. (Which you'll need to do in several applications...7 to 10 days apart).
LofMc