Bacterial Conjunctivitis: This is the most likely diagnosis given the presence of yellow purulent drainage, lid swelling, and conjunctival erythema. Bacterial conjunctivitis is common in children and can be caused by bacteria such as Staphylococcus aureus, Haemophilus influenzae, or Streptococcus pneumoniae. The unilateral presentation also supports this diagnosis.

Viral Conjunctivitis: Although viral conjunctivitis typically presents with a watery discharge rather than purulent, it's still a possible diagnosis, especially if the discharge is not entirely purulent. Viral conjunctivitis can cause significant discomfort and erythema.
Allergic Conjunctivitis: This condition can cause erythema and swelling but typically presents with itching and a stringy discharge rather than purulent drainage. However, in some cases, the presentation can overlap with infectious conjunctivitis.
Foreign Body: A foreign body in the eye can cause irritation, erythema, and discharge. Although less likely given the description of purulent drainage, it's a consideration, especially if the child has been playing outside or with small objects.

Gonococcal Conjunctivitis: This is a critical diagnosis not to miss, especially in cases of severe purulent conjunctivitis. Gonococcal conjunctivitis can lead to corneal perforation and blindness if not treated promptly. It's less common in children but can occur through vertical transmission or sexual abuse.
Herpes Simplex Virus (HSV) Keratoconjunctivitis: HSV can cause a severe form of conjunctivitis that may lead to corneal scarring and vision loss. It's essential to consider this diagnosis, especially if there are any signs of corneal involvement or if the child has a history of HSV infection.

Chlamydial Conjunctivitis: Although more common in neonates (inclusion conjunctivitis), chlamydial conjunctivitis can occur in older children, especially through autoinoculation from an infected genital area. It's a rare consideration but should be kept in mind, especially if other diagnoses are ruled out.
Sjögren's Syndrome: This autoimmune disorder can cause conjunctivitis among other symptoms. It's rare in children and would typically be associated with other systemic symptoms, but it's a consideration in chronic or recurrent cases of conjunctivitis without a clear infectious cause.