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Inner elbow is a popular site for ATOPIC ECZEMA
, also known as FLEXURAL ECZEMA.
Second possibility is SCABIES
, but it does not keep itself to one elbow only, it is seen in all flexure surfaces .
Please see a dermatologist/ homoepath for confirming the diagnosis and starting treatment.
Meanwhile avoid scratching, keep area moisturised.
PS : ECZEMA is not contagious. SCABIES is.