Gastroesophageal Reflux Disease (GERD): The symptoms of spitting up milk, loose stools, and discomfort after feeding are common in infants with GERD. The fact that the infant is experiencing these symptoms despite being on both breast milk and formula suggests an issue with the reflux of stomach contents into the esophagus.

Lactose Intolerance or Milk Protein Allergy: Although less common in infants as young as 4 weeks, an allergy to milk proteins or intolerance to lactose could explain the loose stools and spitting up. However, these conditions are more typically associated with other symptoms such as rash, blood in stool, or failure to thrive.
Overfeeding or Underfeeding: The frequency of feeding every 2 hours could indicate overfeeding, leading to spitting up and loose stools. Conversely, underfeeding might result in discomfort and frequent feeding demands, though this would less likely cause loose stools.
Infection (Viral Gastroenteritis): Although the primary symptoms don't strongly suggest an infection, viral gastroenteritis could cause loose stools and discomfort. However, fever and vomiting are more typical accompanying symptoms.

Hirschsprung's Disease: A congenital condition characterized by the absence of ganglion cells in the distal bowel, leading to severe constipation or, in some cases, diarrhea due to enterocolitis. It's crucial to consider this diagnosis due to the potential for severe complications if not treated promptly.
Intestinal Obstruction: Conditions like pyloric stenosis or intestinal atresias could present with vomiting and abdominal distress. While the symptoms provided don't perfectly align, any suspicion of obstruction warrants immediate investigation.
Congenital Infections (e.g., Congenital Syphilis, Toxoplasmosis): These can present with a variety of symptoms including gastrointestinal issues. Given the potential severity and long-term consequences, they should not be overlooked.

Celiac Disease: Extremely rare to present this early, but an immune reaction to gluten could potentially cause gastrointestinal symptoms.
Congenital Diarrheal Disorders: A group of rare disorders that affect the small intestine and can cause chronic diarrhea from birth.
Endocrine Disorders (e.g., Congenital Hyperthyroidism): Certain endocrine conditions can cause gastrointestinal symptoms among a myriad of other systemic effects. These are rare and typically present with additional symptoms beyond those described.