It sounds most like a common viral upper respiratory event, but yes, you should seek your primary doctor. Would not go to the emergency room.

See your regular doctor. Currently, Influenza is prevalent, but other viruses, not Dengue, and bacterial infections cause acute onset cough and fever.

Dengue fever does not present with cold and a runny nose. If you have travelled to an overseas location endemic for Dengue or other tropical infectious diseases, the specific location may be relevant to your diagnosis. At this particular point in time, your clinical presentation should be considered an influenza-like illness (ILI) until flu is ruled out as the cause. Irrespective of what healthcare provider you see, you should be evaluated while you still have a fever.

These symptoms are not specific for dengue, but could be the common flu, or other upper respiratory virus infection as well. If you do not have more severe symptoms that impact your daily activities, you may not need to go to the ER.