Baggage confused
 

Have booked a economy basic on way out no problem but on my travel conformation it says hand only on way back but the app says economy classic (v fare) on way back so do i have a checked bag or not on the return ? Connecting flight is delta main cabin (v fare) so i think despite what travel agent put on conformation as both apps show main and classic i have a checked bag on way back ? Anyone who has had this happen advice to calm is welcome