Scarlet fever is a bacterial infection caused by group A Streptococcus that is transmitted through the air. Children who are sensitive to the bacterial toxin may develop a rash, although some will not. Infants and toddlers under the age of two are rarely seen with the disease. 

Avoid squeezing the infant's heel if possible. Squeezing causes hemolysis of the specimen. Too much pressure may also result in damage to the tissue. Turning off the bilirubin treatment lights is also important because exposure to the light may alter the bilirubin in the sample. Cleansing the site of puncture is important, and warming the area will increase the capillary blood flow.

The most likely diagnosis in this case is pertussis, also known as whooping cough. This is caused by Bordetella pertussis, a gram-negative encapsulated coccobacillus. It begins as a seemingly normal upper respiratory infection, which progresses two weeks after onset into paroxysms of 5-15 violent coughs followed by a forceful inspiratory gasp, often described as a "whoop." Coughing is often forceful enough to induce vomiting, nosebleeds, or subconjunctival hemorrhage. Croup, pneumonia, and bronchitis are all conditions that include cough, though none of them will generally present with this degree of gasping, vomiting, or blood vessel damage due to cough.

Strawberry tongue (glossitis) and maculopapular ("sandpaper") rash are commonly seen in scarlet fever, a condition caused by group A Streptococcus bacteria, often after a bout of strep throat. The other exanthems listed can all cause erythematous rash, though none are associated with glossitis.

Parotid gland enlargement, fever, myalgia, and tender salivary glands are all indicative of infection with the mumps virus. Symptoms typically last for 7-10 days, though sequelae such as hearing damage and testicular disorders can be long-lasting or even permanent. 

The APGAR score is 8, the child has received a score of 2 under respiration for good cry, a score of 2 under cry reflex for vigorous crying, a score of 2 under reflexes for good reflexes, a score of 1 for heart rate of 97 (under 100 bpm), and and score of 1 for color for acrocyanosis (blue limbs, pink body).

The correct answer is "4." This is correct because the patient exhibits four out of the four Centor criteria for streptococcal pharyngitis. The Centor criteria are as follows:

1) Tonsillar exudates

2) Lack of cough

3) Fever

4) Tender anterior cervical lymphadenopathy

The Centor criteria are used to generate a score based upon the patient's age and number of positive criteria. This score can then be used to assess the likelihood that the patient's condition is due to streptococcal pharyngitis, and therefore to guide the decision of whether or not to treat with antibiotics for streptococcal pharyngitis. In this patient's case, since they are older than 14 and younger than 45, they do not gain or lose points for their age. They get four points total for having all of the positive criteria. Therefore, it is highly likely that they are infected with streptococcal pharyngitis and should be treated empirically with antibiotics.