Most are caused by viruses and will not respond to antibiotics. You may find steam or a variety of over the counter products helpful for coughs. Please ask the pharmacist for advice. You should see a doctor only if your cough is associated with shortness of breath and / or prolonged fevers (feeling cold and shivery) for more than 4-5 days. Coughs usually last 7-10 days, but in some cases can last significantly longer.
Any cough over 3 weeks however, definitely warrants a discussion with a nurse practitioner or a doctor. Call 111 if severely short of breath and 999 if you think you are life threateningly unwell or cannot speak in more than 5 word sentences.