YES it is OK to use a bicarb soda deodorant, but only if it has been carefully formulated to have a lower pH like Woohoo, because we've carefully balanced the pH so it's not too alkaline but it still busts odour with the best of them.
That said, your skin can react if you are using too much, have not properly cleaned away previous applications or have other external irritants like clothing rubbing on the area. Its also good to remember your pits occasionally need some moisturising like the rest of your skin :-)
If you are extremely sensitive which does happen for some, we do have Bicarb free Woohoo Too !!