Okay, perfect information..
So at her age and during molt.. she may (will) benefit from getting less calcium than layer (Usually 4-5%).. which she won't be using as much of as when she was actively laying (taxes kidney long term in non layers possibly causing gout). She will also benefit from a little added protein (layer is usually 16% here) as feathers are made from 90% protein and importantly it's amino acids.. so it will help her build lovely feathers and recover quicker. Chickens being omnivores means plant and animals protein are not created equal.. and they require some animal derived amino acids.. added synthetically to the vegetarian formulas many of us in the US are using.
One of my favorite things to use for molting birds is either a grower feed or a non medicated starter feed (Actually I use Flock raiser but terms being irrelevant.. 18-22% protein and 1-2% calcium) .. the birds LOVE it and it's higher in protein and amino acids plus a few other nutrients as well.. Whatever they call it.. I provide oyster shell and returned egg shells or whatever appropriate calcium supplement is locally free choice on the side for the active layers. If switching or even mixing together with your layer feed is an option for you.. then I highly recommend it.
Short term supplements.. a scrambled egg.. loaded with micro nutrients and a fantastic, palatable, highly digestible treat/boost.. by energy (calorie count) eggs are 34% protein and 64% fat. Half the protein and lots of the nutrient are inside the yolk. Others maybe some canned or fresh mackerel or tuna/salmon.. even a little ground beef (or chicken), etc. Just use it as a supplement and don't go overboard though. Not more than 10% of their total daily intake.
Regarding the purple.. I mean it's supposed to secrete oil and birds often look oddly purple too me. This was the best link I could find showing it.. When I zoom in on the photos they also look purplish on the skin...
https://www.pamsbackyardchickens.com/2014/11/molting-exposes-chickens-preen-gland.html
What do you think in comparison to what you're seeing in person? Is it her preen gland or an ingrown feather or a feather getting ready to erupt?
Is there any stink? Infections usually produce puss (dead white blood cells) which on chickens often becomes a hard plug.. But purple would be more like bruising or just skin with blood vessels underneath.
If I truly thought is was infected.. I MIGHT try to do a warm wash cloth soaked in epsom salt water compress to *try* and help draw anything out.
Otherwise.. I would just keep an eye on it until you can see the vet if it seems like it's getting worse or not improving by the time Monday comes. B vitamins never hurt.. if you have a (human) B complex
on hand.. add it to whatever and offer as it will help boost the immune system, energy.etc
I'd love to see this ripe old gal if you're able to post a whole photo. Big difference between first molt and like 7th!
You mention puffy eyes.. I know they seem to show how we really feel.. but are there any respiratory symptoms like nasal discharge, coughing, sneezing, labored breathing?
Probiotics.. is really anything fermented.. even standard milk left on the counter to sour.. yogurt, kimchi, etc.. some folks ferment their chicken feed or add raw apple cider vinegar and now that I say that.. many feeds actually have probiotics already added to them even when it's not advertised on the label!
What I can see in your photo.. doesn't actually look
angry. Though I can see why are concerned and the purple you mention. Is it giving off EXTRA heat.. like it would if it were a raging infection.. more than body heat (can be 105-107 in chickens)?
If it doesn't look like her preen gland would.. I read you OP again and see you say BELOW the vent.. preen gland would be ABOVE.. so if below then definitely more likely a feather condition and consideration.. SORRY.. this is how clues reveal themselves to me, it's a process of elimination and missing a single detail can be so key!
Reset.. My questions will still help, I think overall still. It doesn't look life threatening..
