Are you sure that it was baking soda, not washing soda, a
much more potent chemical.
Absolutely, it’s used inside your mouth, so it must be something
harmless if it’s swallowed. The baking soda is used as an
abrasive, not as a chemical. A little tends to splatter about
your face after it rebounds from your teeth. A very nic e way to
have your teeth cleaned/polished.