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Generally speaking, pimples shouldn't bleed. The only reason they bleed is if you pop them, and you know better than to pop them because that can leave a scar and also spread bacteria. But let's say you made a mistake just this once and you have a pimple that is bleeding. There are a few steps that you should take to stop the bleeding and clean the area.
Hold a clean facial tissue to the pimple and apply gentle pressure until it stops bleeding.
Gently wash the area with a mild cleanser and lukewarm or cool water and pat dry with a clean towel. You want to clean up any bacteria that were present inside the pimple and spread when the pimple burst.
Dab a small amount of acne medicine onto the pimple. Effective ones to look for contain salicylic acid or benzoyl peroxide, because these are good pimple-fighting medications and will help clear out the bacteria.
Apply ice to the pimple if swelling occurs and hold it on the area for 10 minutes. Then dry it off with a clean towel and re-apply the acne medication. If the zit starts bleeding again, hold a new tissue against it and apply pressure until the bleeding stops.
Instead of popping a pimple when the head of a pimple is white and filled with pus, apply a very warm compress and then dab some acne medicine on it. This will help the pimple go away without popping it.