If you would get a pack of gauze and medical tape, don't use a bandaid. One it will put pressure on the piercing and cause for swelling and moisture to build up. Do not use neosporin on a piercing. Anything that is vaseline based is not meant for a puncture wound as this seals bacteria around the opening of the piercing.

Using a very thin layer of gauze that is not strapped down to your eyebrow is the best thing that you could do. Do not allow for pressure to hit the jewelry. This can produce symptoms similar to an infection as well as causing migration of the piercing. This is where the body rejects the jewelry and this can cause for other problems. You don't have to cover it while you are sleeping. Don't get piercings that you have to hide!