I've cared for combs damaged from pecking, and, I think, also getting caught on the chicken wire.
I use a saline solution to wash it (boil a cup of water with 1/4 cup sea salt in it, cool, then pour in jar)
then put on a balm to protect it (I use a home made salve with tea tree oil and herbs in a beeswax base, but I think bag balm, or even chapstick would be helpful)
On the first comb I cared for, I used peroxide to clean it then Neosporin to heal/coat it. I found those products to be too harsh - they dried the comb out, leaving it more fragile. I found iodine to be too harsh also.