Fever
Unlike older children, it can be difficult to tell when a newborn is seriously ill.That is why doctors routinely do a septic work-up on infants who are under two or three months old when they have a rectal temperature that is at or above 100.4 F.
Be sure to call your doctor or seek medical attention if your baby has a fever.
Umbilical Cord Issues
The biggest issue with a baby's umbilical cord is that it sometimes doesn't fall off as quickly as a parent would like. Keep in mind that your baby's umbilical cord may not fall off until your baby is three or four weeks old. See your pediatrician if it is staying on longer than that or if it is showing any signs of infection. An infected umbilical cord may have a foul-smelling discharge and/or the skin around the cord may be red and tender.Blocked Tear Duct
As your baby starts to make tears when he is about two weeks old, if he has a blocked tear duct, you may notice a lot of extra tearing. The tear duct normally drains tears from the inner corner of your baby's eye into his nose. When blocked, the tears pool in his eye and drain onto his cheek. Or the eye becomes crusted and matted when the tear duct gets infected.Fortunately, most cases of blocked tear ducts go away on their own. You may have to treat your child with nasolacrimal massage (in which you massage the inside corner of your child's nose two to three times a day), cleaning any discharge or matter in the eyes with a warm washcloth, and occasional topical antibiotics, until it does though.

