No one can tell you over the internet what ammunition may or maynot be safe in a given gun.
Unless special ordered with longer chambers, your 1928 vintage Parker Bros. 16-gauge started life with 2 7/16-inch chambers intended for the then "standard" 2 9/16-inch 16-gauge shells. By 1928 we were well into the progressive burning smokeless powder, high velocity loads and if your gun was being used at all it probably saw plenty of these --
Second style 16-gauge Super-X load side.jpg
HIGH VELOCITY 16-gauge, 2 9-16-inch, #6.jpg
While the gun if in sound condition will handle them, whether one wants to subject 95-year-old wood to the recoil forces of such loads is another question.
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