it's scary, have been there wit my dd who is now 7, and thankfully is growing out of the asthma cough.
From about one year old she coughed all night every night, till she was about 3 1/2-4. Every time she got a cold, (which was alot of the time) it went straight to her chest. We have had croup, infections, asthma, the lot.
yet, I am sonvinced that with the gp looking after you, that you will go down the routes you need to. it's very distressing i know.
There are lots of threads on mumsnet, if you have a search, about parents going thru this.
Just know you arenot alone, and tbh there are lots of bugs going round atm which seem to knock our kids out.
It will get better, in time.