Down Syndrome: This condition is characterized by early teething, poor muscle tone which could explain the difficulty in lifting the head, and an increased incidence of periumbilical hernias due to weakened abdominal wall muscles.

Beckwith-Wiedemann Syndrome: This genetic disorder can cause early teething, poor muscle tone, and an increased risk of omphalocele or other abdominal wall defects, which might be related to the periumbilical hernia.
Prader-Willi Syndrome: Although more commonly associated with hypotonia and feeding difficulties in infancy, some cases might present with early teething and could have abdominal wall defects, making it a consideration.

Congenital Hypothyroidism: This condition can cause developmental delays, including poor head control, and is associated with constipation and abdominal distension, potentially leading to hernias. Early diagnosis is crucial for treatment and preventing long-term developmental issues.
Spinal Muscular Atrophy (SMA): A severe condition causing muscle weakness and wasting, which could explain the poor head control. While not directly linked to teething or hernias, its severity and impact on quality of life make it a critical diagnosis not to miss.

Ehlers-Danlos Syndrome: A group of disorders that affect connective tissues supporting the skin, bones, blood vessels, and many other organs and tissues. Some types can lead to early teething, joint hypermobility, and potentially an increased risk of hernias due to tissue fragility.
Marfan Syndrome: Although more commonly associated with tall stature, long limbs, and eye and heart problems, some infants might present with early teething and could have an increased risk of hernias due to the connective tissue disorder affecting the abdominal wall.