I have a nasty red rash on my wrist from my apple watch band.

What kind of band, and what is the metal clasp made from? It sounds like you have an allergy to whatever the metal is. Most common metal allergies are Nickel and brass. Brass is frequently used as a cheap substitute for gold. Nickel is a component of many metal alloys. And you can't test it with a Nickel coin, because it isn't made from Nickel. You might want to visit an allergist, who can test you and then you will know for sure.

won't that hurt the band?

You can put nail polish on a human body so I can't imagine it could do much harm to a silicon band. Besides, which is more important, the band? Or your skin? I assume that you mean the sports band. I'm suggesting that you put a coat of nail polish on just the metal button on the side where it touches your wrist. If you don't like the idea of nail polish, white school glue ought to work as well. It just won't be as thin a coat and will probably take longer to dry.

I would not suggest using nail polish remover on the band.

The rash is only located where the metal circle touches my skin. I have cleaned both surfaces and have switched wrists to test it out. I now have a rash on both of my wrists.

Try covering the circle with clear nail polish.

You appear to be allergic to the materials in the watch. See your doctor. You say it's from your watch band, then you say it's from the bottom of the watch?

I've been wearing my Apple Watch for a couple years now and have never gotten a rash. If I did, this isn't likely where I'd come for guidance though. You may have an allergy to something on the back of the watch. I'd seek the medical care of a good dermatologist to have the rash looked at.

See a dermatologist. Good luck.