You have not stated the weight and size of your carry-on bag
Not all airlines have same rules. A sample from EK
http://www.emirates.com/au/english/p...age_rules.aspx
First Class and Business Class customers are permitted two pieces of carry-on baggage: one briefcase plus either one handbag or one garment bag. The briefcase may not exceed 18 x 14 x 8 inches (45 x 35 x 20cm); the handbag may not exceed 22 x 15 x 8 inches (55 x 38 x 20cm); the garment bag can be no more than 8 inches (20cm) thick when folded. The weight of each piece must not exceed 7kg (15lb).
Economy Class customers are permitted one piece of carry-on baggage that may not exceed 22 x 15 x 8 inches (55 x 38 x 20cm) and must weigh no more than 15lb (7kg).