First cold... drooling ?

Sa

My baby is sick for the first time. He has a cold. He is also drooling EXCESSIVELY. He’s SOAKING his onesies and drool just comes out of his mouth constantly. He has zero teeth so far. Do you think the drill is just because of the cold/breathing through his mouth or is he likely also teething? Did your baby have drooling like that with a cold?