No it is not normal.

It could be from the bag hitting without wraps, but I am also seeing a lot of folks in the gym wrapping their wrists insufficiently.


You are not going to like my avice, else you would not have asked: Go see your doctor.

Make sure that a) it is nothing serious and b) you aren't continuing to damage it.

Then, when it feels better (or after you have rehab'd it) always wrap your wrist as part of your hand wrapping.

Also, try to find a water bag to hit in the gym -- most serious gyms these days have a choice of bags from rock hard to really mushy. Find the ones that don't cause pain when you start hitting again.