"Supposed to" gives more information than "should". It indicates that there is an obligation (like "should") but also a doubt or uncertainty about the fulfilment of the obligation. e.g. "I am supposed to make dinner for my wife later." does not mean the same as "I should make dinner for my wife later." BUT "I am supposed to make dinner for my wife later but I don't feel like it." means the same as "I should make dinner for my wife later but I don't feel like it." So, when you explain the doubt, you can use either option.