How can I treat dry skin around my mouth and chin?

I would like to know how to treat the dry, flaky skin I have around my mouth and chin. I have been applying coconut oil and hydrocortisone on those areas. I have also stopped applying makeup and I use a fragrance-free face wash. For example, I use Neutragena Oil-Free Face Wash. I don't know what could be causing this and I would like to know how to treat it. Thank you.

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