I am experiencing persistent dry cough since the past two weeks. I have tried war water gargling and take Nyquil Cough suppressant, but the symptom is not improving. Should I see doctor now?

You're getting close. Dry coughs are a little less worrisome than productive coughs (when you cough up plegm/sputum...or even blood!) Dry coughs are associated with viral illness, sinus issues, smoking, allergies, asthma, lung irritants, medications, reflux. Really emphasize hydration: water, hot drinks, steamy showers, humidifiers. Use lozenges. Most experts say adults can watch a dry cough for 4-8 weeks before eval.
Yes. However these infections can last 10-14 days. Here are some simple hints: Force fluids x 8-10 glasses/day: 50% electrolyte rich fluids, 50% clear broth, bullion, consume .Warm water gargles, nasal saline mist, hot tea and honey, Hot steam showers, Cold-Eze Lozenges, Tylenol (acetaminophen) 1-2 TABLETS every 4-6 hours as needed for fever greater than 100. Tea with dark brown honey OK to use Robitussin DM 1-2 tsp.