Foreign Body Aspiration: Given the acute onset of cyanosis and the fact that the child is teething and thus likely to put objects in his mouth, aspiration of a foreign body is a highly plausible cause. The child's mild distress and inability to relieve cyanosis with supplemental oxygen support this diagnosis.

Pneumonia: Although the child does not have a history of congenital issues, an acute infection like pneumonia could lead to cyanosis, especially if it's severe. The discomfort and mild distress could be indicative of respiratory infection.
Anaphylaxis: Although less common in this context, anaphylaxis could cause cyanosis due to severe respiratory distress. The recent introduction of new substances (e.g., topical analgesics for teething) could potentially trigger an allergic reaction.

Congenital Heart Disease (Undiagnosed): Despite the lack of history of congenital heart issues, some conditions might not be apparent until later in infancy. Conditions like Tetralogy of Fallot could present with cyanosis that is not relieved by supplemental oxygen.
Methemoglobinemia: This condition, which can be caused by certain medications (including some topical anesthetics used for teething) or foods, leads to an abnormal amount of methemoglobin in the blood, causing cyanosis that does not respond to oxygen therapy.

Cyanide Poisoning: Although rare, cyanide poisoning can cause cyanosis due to the inhibition of cellular respiration. This could potentially occur through ingestion of certain substances.
Cardiac Arrhythmias: Certain arrhythmias could lead to decreased cardiac output and subsequent cyanosis. These are less common in infants without a history of cardiac issues but should be considered in the differential diagnosis due to their potential severity.