[Acne] Pimple 'core' remains after pimple has started to heal - is extraction the only option?

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A closed comedone became inflamed but has mostly gone down. However, the 'core' of the pimple, aka the thing that caused the inflammation, is still partially there. Extractions never go well for me - do you think that using BHA and retinoids will help it come out? I don't want the pimple to kind of 'heal' with that thing still in there.
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Submitted by Sleepyrabbitz