Shoulder pain caused by messenger bag?
Take a look at your riding position.  When I was much younger (about 10-12 years ago) I used a messenger pack all the time while in an aggressive riding position (e.g., track bike / road bike) . In that position I found your lower back supports most the weight of the bag.  In a more upright position it pulls on your shoulder more.  As a test, try walking around for a while with one... it sucks.

If you prefer a more upright riding position (no judgement!) then a messenger bag may simply not be the right fit -- sorry pun intended, my bad.