https://www.backyardchickens.com/t/33903/scaly-leg-mites-need-best-easiest-quickest-solution-scaley
here is a nice link for reading about scaley leg
I am really not seeing lifted scales in the pics. But if you see them with your eyes as you are there looking at the birds then I'd go ahead and coat the legs.
I personally use mineral oil (vegetable oil works too) for two weeks, dipping each leg every day to smother the mites. Toward the end of the two weeks I do it every other day.
Also I have learned that smearing oil on the combs/wattles is good too as these mites attack the facial area sometimes.
The swelling concerns me and I don't know what that would be.
This is what I would do. It will not hurt for sure. I am puzzled by the swelling though. Maybe do an epsoms salts soak followed by the oil on the legs and the head...it won't hurt anything for sure and it may make her legs feel better.