Missing feathers on RIR

Are any others missing feathers? Is she bare on her underside as well? The missing feathers on her bottom could be an early sign of parasites, and there is a parasite (Giardia) that causes them to pick at the feathers on their backs, but usually on the shoulders. https://www.backyardchickens.com/t/898440/massive-feather-loss. The skin looks very inflamed. Perhaps there's a skin infection? We once had one with an infected oil gland who gradually pulled all the feathers out of her tail because it hurt. A course of antibiotics took care of that. https://www.backyardchickens.com/t/949949/red-swollen-tail. We haven't had roos with the hens, so I can't help there.

I haven't noticed anything like this on any of the other 15 hens. I will look up Giardia. I'm not sure if the skin is so inflamed from the sun or from her recently picking. I notice that in the evenings its not nearly as red. Do you think the hen saddle would take care of it? I guess it couldn't hurt to try it first and see if that fixes it.
I'm new to chickens, well it's been about a year. Still on a big learning curve...
About the antibiotics... How do you administer antibiotics? How long do you need to wait to eat the eggs after they have been administered? I'm guessing I would have to find a vet that treats chickens, what is an average price for a visit? I'm also thinking if I did use them (the antibiotics) on her I would have to separate her from the flock since I would have no idea which egg is hers. I'm worried that would stress her out too, just being separated.

What do you dust them with?

If it's just a skin inflammation, a systemic antibiotic may not be necessary. I try to avoid them until it becomes necessary. Try an antibiotic cream. I found that triple antibiotic ointments based on petroleum jelly seem to bother them. If you don't see improvement, that would give you some information to work with. The inflamed oil gland was obvious; swollen and red and tender. She was pulling her tail feathers out. I would suggest you also try the hen saddle (there are some instructions for making one on here somewhere), and see how that affects the area. One vet used a piece of tape to look for parasites or bacteria. He pressed it against the skin, pulled it off, and looked at it under a microscope. Vets here cost $65 for the visit. Treatments and medicine cost more.

To find mites, go into the coop in the dark (if it's accessible) with a flashlight and turn it on suddenly. If they are there, you will see them scurrying. Some you have to look at the base of the feathers to find. Mites are usually on everyone, though. There are poultry dusts with permethrin (or pyrethrum, not sure) which is a natural insecticide and repellent. I put it in a sock and lightly patted it over them while ruffling their feathers. Try to keep it from their face.

I have found that bare area on the bottom to usually mean internal parasites, but for a recent one it was an egg laying problem. Is she laying eggs? Safeguard is a very safe medication for parasites. It's difficult to overdose, but you do have to avoid the eggs for 7 days (per European Union regulations). If you have different breeds laying different color eggs, it's easiest to treat one breed and avoid those eggs, then treat the others and use the eggs of the first batch. That does increase the risk of the first batch getting reinfected.

Hope some of this is helpful.

Your response was very helpful. I'm not sure if she is laying eggs or not, we have 16 other hens. I might try to get out there and visit more often and see if she is in one of our boxes. If that fails I guess I can separate her for a bit and see.

I often bring one in in a cat carrier to watch if something seems off. I can see if they're eating, see what their droppings are like, and look for any other odd behaviors. I try to keep them for as short a time as possible. Even a couple of days can make it difficult for them to re-integrate with the flock. We have some permanent "infirmary girls" in the barn who were out so long due to serious illness or injury that the flock refused to accept them back. Had to keep them out to save their lives (literally).

Thanks for the information and help. I really appreciate it.