Unsure

Ask for a referral to a pulmonologist (lung specialist) for a thorough diagnosis starting as others have said with a CT scan (have you even had an X-Ray to discount cancer/lymphoma?). I doubt your GP will resist when you remind him of the number of infections a year you are having and that you have only been given a generic diagnosis of lung disease. Start polite and if you meet resistance, ask what precisely is his/her diagnosis, chronic bronchitis, bronchiectasis, COPD, lymphoma, lung cancer etc? If there is no relenting then ask what are the appeal procedures for getting specialist attention. If you are polite and insistent I'm sure you will be referred. Don't be fobbed off with a "we are waiting for results of sputum saples" - it seems to me they are jumping in way too far down the road of analysis if that's where they  started (but I'm not a pulmonologist myself).

Not sure about the doctors hate internet comment. I have always found them to be receptive to responding to a non-confrontational use of information you have obtained from wherever. I believe that with the proper attitude medics prefer to have a session with an informed patient rather than one who is ignorant/passive. Boring as hell for them t have a one-sided working (non-)relationship all the time.

Change GP practice (or ask for a different GP in a multi-discipline practice) if you have doctors who are just prescription writers. My former GP practice in Leeds (now living in Thailand) was a real mix of fantastic doctors, enthusaistic starters and burnt-out pill-pushers, but generally I was very impressed with the practice. Can be difficult to break into the list of the fantastics though!