Is eczema around the ears bad for ear piercings?

So I have rather severe eczema around both my ears for some reason. It's a skin rash for which the cause is unknown. This is what the internet told me, and a doctor who looked at it said the same.

I've already had a lot of people tell me that there's white stuff around my ears, and I've always had to explain that it's just eczema. It's an allergy that I have no control over. I was thinking that getting my ears pierced would lead to even more attention to my eczema.

Not only that, but I'm afraid that the eczema could lead to infection in the piercings if they somehow come into contact. Could that really happen? There's not really a cure for it. Is there anybody here with ear piercings and eczema around the ears that can explain what it's like?