There are many causes of cough but the most likely cause in a young man, in a young man with a history of allergies (“a runny nose and watery eyes”) would be asthma or allergic inflammation of the nose resulting in post-nasal drip. The medication you’ve been given, Galpseud, is a combination anti-histamine/decongestant, a reasonable choice. A trial of asthma treatment would be reasonable at this time but since there are a number of other, more serious, often treatable causes of cough, you should also have a chest X-ray.
Further testing for asthma to include pulmonary function tests, with and without a bronchodilator medication, could also be helpful to “pin-down” the diagnosis of asthma.
Good luck
Forgot to mention that my upper nasal tract feels blocked for all that time period too. Sometimes when i clear the mucus, it still feels partially blocked also.