I have symptoms of cystic fibrosis. Is it possible to start show the symptoms in my 30's?

Yes. Yes it is possible. Presentation of cystic fibrosis varies greatly, and it is possible, depending on your specific mutation (and other factors) to present at a later age. In order to prevent late diagnoses, all states now have a newborn screen in place for cystic fibrosis.
Yes. It is possible, although at 30 other causes of bronchiectasis and chronic cough should be considered as well (mycoplasma pneumonae, etc). If you have the classic pancreatic, bowel, and lung disease genetic testing is always worth considering.