It seems that you mau be having omphalitis...infection of umbilicus
leading to abscess.Consult dermatologist
for comlete examination and diagnosis.
If there is abscess, incision and drainage
may be done.
Strong antibiotics with anti inflammatory drugs may taken.
Apply antibiotic cream.
For diarrhea, consult physician.
Anti diarrheal drug like lomotil may taken. If there is dehydration
, saline pint may be taken in hospital.
I hope you got my answer.
Dr. Ilyas Patel MD