How long does it take for a rash from neosporin go away. it has made my skin red where it was applied?

When skin is in contact with a substance that you are allergic to (or a chemical irritant) it can take 2-4 weeks for the rash to go away. If it is itchy, do your best to avoid scratching your skin - that will likely prolong the rash and could also lead to a skin infection. Don't repeatedly wash the area either, which can dry out the skin and further irritate the skin as it is trying to heal.