I think that the line in the first stanza is actually "shoulda wore my wedding ring"- i.e. the protagonist should have kept his wedding ring on rather than stepping out on his wife on those 15 nights/16 days.
I think that the line in the first stanza is actually "shoulda wore my wedding ring"- i.e. the protagonist should have kept his wedding ring on rather than stepping out on his wife on those 15 nights/16 days.