As others have stated have the bore measured. Further measure the chambers. It was common on many guns chambered for 12ga cartridges in the days of cork, paper, or felt wads to be bored tighter to give a better seal.

A 13 ga chamber would be rare, but it is likely a 12 chamber with 13 bore

I have several 13/1 guns which handle 2 1/2 12ga loads w plastic wads without issue.

Michael Dittamo
Topeka, KS