Hi @cheri braithwaite so sorry you're having so many problems with Killian thank you for rescuing him <3 Does he come from a rescue or is he a private rescue? Normally the rescue makes sure the dogs are healthy before adopting out. if he's from a rescue I'd contact them and ask them, they should know what is going on with him since you basically just got him.
The skin issues can be many things... could you take a picture maybe? The vet can do a skin scrape, that should show exactly what it is.
How old is Killian? Sometimes dogs can develop eye issues with age, it could be Entropion, it's when hairs are growing where they shouldn't and they scratch the eyes... The vet can check that and you could probably see it yourself even if Killian would let you have a close look.
Maybe the antibiotics clears most of his issues up, lets hope it helps
Keep us posted