Sadly Delta have very few, if any agents, who enforce any restrictions on carry-ons Occasionally they will actually try to limit people to two (and get told off by DYWKIA flyers who think that "Diamond means I can bring on as many bags as I want"

However, since it sounds like the OP doesn't have status they could possibly be in the last boarding group and you have a very good chance of having to gate check your luggage then because of the lax enforcement....