How are newborn acne and an allergic reaction different?

Take to pediatrician: I would certainly take my child to a pediatrician to see if it is an allergic reaction.

Doctor can evaluate: Baby rashes are pretty common, but hard to describe in words. Babies commonly get erythema toxicum spots after birth, which can resemble acne (but they don't open up nor ooze). Later, they can get baby acne, which resembles teen acne, but baby acne spots generally don't break open. A pediatrician or dermatologist can look at the rash to help decide what it is.

Use pictures: I always encourage my parents to use credible websites to compare rashes before they come into the office. Email acne is acne and can be very expensive, an allergic reaction would usually be more immediate and may go away with treatment very quickly, where acme is a self resolving problem overtime.