Strange cough that's in my family?

Okay, it started out as my mom who had the cough. Then after a few months, I got it. Then my brother got it only a week after me. My dad hasn't gotten it though.When my mother went to the doctor, they said that she had asthma and/or a lung infection. When I went, they told me it was simply a cough and should go away in 6-8 weeks. So far (three months later) it hasn't gone away. My brother has not gone to the doctor, because it's not as bad as our cough. We are like 90% sure we have the same thing because it's all the same symptoms. Mostly just an extremely bad cough were we sometimes cough up phlegm. None of my friends have it, and I'm pretty sure none of my mom's friends have it either, so my mom thinks it's something in the house. I disagree because I cough the same at school as I do at home, sometimes worse. Any idea of what it could be?