Don't worry about the red skin, it is just a reaction to light but is not sunburn.
Try stepping up the protein you are giving her. You should be feeding something that has 17-18% protein, preferably animal protein to her. If your feed is low in protein, she will struggle to grow feathers. If the follicles are not damaged and the other hen is not pulling out what she is trying to grow, then the protein should help. With low protein food you can also supplement with dog roll or cat food. The dry cat food you are feeding may be loaded with carbohydrates rather than protein. Just make sure that either cat or dog food is not high in salt as hens can't process high amounts and it will damage her kidneys. Meat scrap or fish scrap also good sources, but the fish needs to be pressure cooked to make the bones go soft/brittle and should be fed twice a week at about 100grms per hen (exact amounts not necessary) Let us know how you get on.