It is possible to get diagnosed in later years, I was dx'd at 33 yrs old...I too thought it was "asthma" and always had respiratory problems with frequent infections. What made my doc think CF was a possibility was when I grew out CF bugs from my sputum. That along with my digestive problems raised red flags and so I was tested with sweat as well as genetically and came up as borderline with my sweat test (50) and one real mutation and variant that may or may not be disease causing. Those results along with my clinical picture landed me the CF diagnosis. I stress the importance of getting evaluated for CF because proper treatment is so important to help with lung function as well as prevention of infections. I am on several different nebulized meds (one antibiotic, 2 mucolytics, brochodilator) and puffers along with many other meds to keep me healthy. It is hard work, I know that I would be much worse without all of these interventions..including daily chest physio to clear my secretions. As far as CF running in the family, I am probably the first to be diagnosed and I have a big family. But the more I poke around my family's history, the more I believe that some of my relatives that had passed early from lung related issues had CF. CF is a disease that requires two mutations, one from each parent so it is possible to have several carriers in your family. There is a 1 in 4 chance of getting CF when both parents are carriers. There is no chance of CF if only one parent is a carrier.
I would go see a doctor who specializes in CF, in a CF accredited center (go to CFF.org to find a center nearest to you) and they will evaluate you. You will probably get a sweat test, the first step usually....most CF'ers have sweat tests >60, some like myself will fall in the borderline range (40-60) and then there is negative results (<40)...Keep in mind that there are some CF'ers who even have normal sweat tests but genetically, they do indeed have CF. The next step usually is a genetic test where they will test for mutations..CF has over 1600 mutations, more are being found yearly. Ask for a complete analyisis of the gene.
I hope this helps you,