What are my chances estimated of lung cancer at 22? I don't smoke or drink. But woke up with a cough and feeling of mucus in chest?

<1% over next 30 yrs. The risk of developing lung cancer in the us by age group: http://www.Cdc.Gov/cancer/lung/statistics/age.Htm . At age 22, yours is less than 1 % over the next 30 years. It is much higher if you start smoking or work/live in an environment with great exposure to passive smoke, asbestos, mining dust, or radiation like radon.
Small. Smoking is by far the number one cause of lung cancer. If you haven't smoked, it makes lung cancer less likely. That's not to say nonsmokers dont get lung cancer. Far from it. But it makes it less likely. A cough with mucus is typically a bronchitis. But, if you are concerned then definitely get checked out.