Yes, it's common, and I have regular mucus build up because, well, my cilia don't clear it well for me. :)
As rscho mentioned, you should definitely bring it up and see if you can get a referral to a specialist. I see a pulmonologist regularly to keep an eye on it. The term Kartagener syndrome (SI + PCD) may ring a bell to them more than PCD will.
I was misdiagnosed as a kid as having asthma (or something like that, I don't remember this well), and doctors prescribed an inhaler but it had no effect. My parents had me seen by a pulmonologist which then led to a diagnosis.
The parent is correct. This is a common association in situs inversus, and you should seek specialized care. Your GP will probably not know about that (it's extremely rare), so if you have to insist, do so.
Do you often get chest infections too? Apparently that's very common as it is with me and those who have DC or Situs Inversus.