Toxic levels of baking soda
Baking soda is sodium hydrogencarbonate, $\ce{NaHCO3}$, also known as sodium bicarbonate.

The only toxicological data in the GESTIS database on hazardous substances
 is a LD50 of 4220 mg/kg for the oral uptake by rats. There are no data for dermal uptake. 

In water, $\ce{NaHCO3}$ is weakly alkaline. I do not know whether it might cause skin irritations, particularly in more sensitive regions, such as armpits. 

In occupational safety, I'd recommend to avoid skin contact and use personal protection equipment when handling it.