Get a letter frm the doctor stating the name/s of the medication and the reason (type of illness).
Check with Emirates locally with the letter from the doctor and get a response from them in black and white. They should be able to help.
Another option is to ask if they have an airside/transit hotel so that you can break the journey there.
Finally declare meds on arrival Dubai and be prepared to source locally if the meds get conficated. Medical insurance to cover this.
Good luck.