Welcome to Healthcare magic forum.
Your baby seems to have most probably a dermatitis with superadded infection .Since the stools are greenish and the baby is not on any medication its most probably a infective diarrhoea which needs to be treated with antibiotics.
The best way to confirm the diagnosis would be a physical examination by his pediatrician
.The doctor after confirmation may precribe a course of broad spectrum antibiotics like cefixime or amoxicillin
.For local application mupirocin or fusidic acid
combined with topical steroids and emollients may be prescribed. Alternatively if indicated he might try anti histaminics like chlorpheniramine
for symptomatic relief before starting any antibiotics.
So the next best step is to get your child reevaluated before starting any medications .
Remember that infection is better prevented than cured in infants to be on the safer side.So, yes the situation doesn't seem very worrisome at present but it warrants further investigation for confirmation .
Hope that answers your query.