Hi there and thanks for the post.
I know that a lot of people can have skin reactions to dogs like Shar pei's. I don't know if Chows have the same problem but this may be the cause of this problem. I think it is more likely to be a some characteristic of the coat that is causing you to react not something on the coat.
If you are worried you may want to ask a doctor or skin specialist if they have ever had anything like this before.
Good luck but for the mean time it may have to be the antibacterial soap
Todd