Could I have a lung tumor if chronic cough?

Possibly... The most common etiologies of a chronic cough are bronchospasm from any cause, gerd, post-nasal drip or a combination of factors. If you have smoked, there is a risk of malignancy. So, if you have a cough for 3 weeks or more, you should see your doctor and find out the etiology of the cough so treatment can be rendered. If you currently smoke, your doctor can help with smoking cessation as well.
Could be. Cough with blood in the sputum is strongly suggestive of lung cancer. Cough that has gone on for months is more likely to be due to chronic bronchitis. It would be prudent to see your doctor for examination and tests, if needed.