Here is the obvious thing that everyone is missing...
If 16# is causing you shoulder issues or aggravating a shoulder injury you have 3 choices-
--Continue bowling in pain with 16# and likely do more damage. IMHO, worst choice...
--Stop bowling all together... Not a very popular option either, but at least the shoulder should not degrade further as fast.
--Drop to 15# or 14#. You'll still be bowling and there is very little, if any, advantage to using 16# equipment in the modern game. For every pound in ball weight you drop, you put 5 times (If I recall correctly) less force on your shoulder while in motion.
Try a lighter ball... just remember that you will have to adjust your game. If that's too much to handle, well, there is always option #2