Can you hit a nerve while injecting the masseter muscle?

From your description, I think it is unlikely that any nerve was hit during the Botox injection into your masseter muscle.  It is possible the muscle itself was hit and just got a bit of a bruise below the level of the skin.  In this case, some pain on that side would be possible even though a bruise may not be visible on the skin.  I would expect your issue to resolve completely fairly soon.  

It is possible, though rare, that a nerve could be hit during Botox injections. It's best for you to return to your injector for an evaluation. If this is what occurred it's not likely to cause permanent damage.

Thank you for sharing your excellent question and I am sorry to hear of your symptoms. It sounds as if either a bruise or muscle irritation occurred during your injections and this should improve given additional time.  Hang in there and inform your injector of your discomfort.  They can provide you with additional reassurance. 

Although it is always possible to hit a nerve with injection, the most likely reason for your discomfort is a bit of bleeding into the muscle which will completely disappear on its own

Chances are very small that a branch of a nerve was hit but it is possible. The most likely scenario is that you have a small bruise in the muscle and it will continue to hurt until it's resolution. Applying moist, warm compresses will help quite a bit. Good luck for New York City