I have a "productive cough"

[OpenMe]

I've had it for almost a month. it was quite painful on my chest for the first few days but since then it's just been mildly annoying, not even enough to keep me awake at night and I feel fine in myself.

However, it is still producing all this revolting phlegm and sounds disgusting when I cough. i'm really quite self-conscious about how anti-social it must seem to be out in public. I've seen the ads saying you should see the doc if a cough lasts more than 3 weeks, but if you're basically well, does that apply?

Yup. It could be an infection that will respond to antibiotics. (it might not be but its worth a try).

Yeah it still applies even if you feel fine, book an appointment!

Also though, the only way to clear all that phlegm is to cough it up. Have you been using some chesty cough medicine to help this along?