How to tell why your baby has sniffles: allergies or a cold?

Pediatrician. It's always safest to bring a baby to the Pediatrician for a formal evaluation to make sure it's just allergies and not an infection.
There are ways... Typically an allergy is not associated with a fever. This is a big clue of a viral infection. Otherwise we usually look for other symptoms, i.e. Sore throat, aches/pains, and cough that are typical signs of a viral infection. Colds usually last 7-10 days where allergy symptoms may go on for weeks sometimes. The typical allergy related symptoms include a clear runny itchy nose and/or eyes.