I've had cough for about 3 months mostly at night, with itching and tightness of the chest, coughing up of colourless sputum, is it asthma?

Probable: It is likely that you have asthma but you really need to see a doctor to confirm the diagnosis and be treated accordingly.

Many possibilities : Including asthma but also GERD (gastroesophageal relux disease) or post nasal drip. As these other forms of cough can be notoriously worse at night related to how we are more predisposed to severe reflux (which csn even present only with a cough!) or post nasal drip based on how our anatomy changes with our body position. Sounds like you should review this with your doc.