How can I tell if my son is having a newborn rash or an allergic reaction?

Rash most likely. Newborns have a variety of skin issues.Most have a bump on a flat red bloch rash that peaks @ 4 days & fades in a week or so. Most have dry skin that flakes a lot.Withdrawal from maternal hormones produces a pimply outbreak that increases over weeks & fades after 4-5m. In three decades, i've never seen a newborn with an allergic reaction. If you are uncomfortable with what you see have baby seen.
See your doctor. If he is newborn and you are at all worried about allergic reaction he should see his pediatrician immediately.