I have a persistant cough for the past two weeks. I'm asthmatic but it doesn't fel like I need my inhaler. I ben taking nortuss (cough syrup) and syrte?

See your doc. Cough can be caused by multiple underlying factors which requires a thorough evaluation with a physician.
Try your inhaler. If you have asthma and are coughing but don't feel very bad & your inhaler doesn't make the cough better for a few hours then its probably not an asthmatic cough. Coughing could be due to post nasal drip from allergic rhinitis or sinusitis, from inflamed throat & vocal cords, or from acid reflux. A symptom that has lasted for 2 weeks & can't be explained deserves a visit to your doctor.