I think what your discribing actualy is a muscle injury although u dont htink it is.
Correct me if i am wrong....but the pain u feel is NOT on the underside of your forarm (the side where the major veins are) but ontop of your arm the (hairy side).
If so then i beleive it is the thin band of muscle that runs over and next to the bone( not sure on the terminology). The feeling is very similar to "SHIN SPLINS".
If this is so then it caused by shock waves going up your arm caused by when your hand impact on the bags when u punch. Much the same way shin splints are caused by runnning on a hard surface and shock travels up your shins.
If this is so as i said above then its pretty normal and u have to condition yourself just like a runner would have to in order to avoid shin splints.
Take it easy when it hurst...prob best not to hit the bags but if u must hit them very lightly til u recover. After u recover go at the bags as normal and over time your muscles will start to strengthen and u wont have the same feeling.
If this is not the case then i am not sure what u have.