My one old month baby has eye infection on both eyes he's been in an ointment for a week and still has the eye infection. what could it be?

Tear ducts plugged: During an eye infection some of the debris can drain into the narrow channels that empty the tears into the nose.When they are plugged, you can have persistent crusting at that age. A followup visit with your doc may be the best way to assess the issue.

Possible NLD obstruc: Up to 6% of infants are born with a blocked tear duct (nasolacrimal duct). Blockage of the normal drainage of tears can result in eye infections. Many blocked tear ducts in infants open spontaneously, however, some require surgical opening. You should have your child examined by an ophthalmologist to determine if this is the cause for your baby's chronic infection.