Have you tried chesty cough mix from the chemist? They can really help shift it, or at least keep things moving, IYKWIM.
Probably nothing drastic will happen if you've already had it for 2 weeks, but make sure you do go to the Drs as it can (I believe) develop into pneumonia if not treated.
Go see the chemist and ask their advice in the meantime, and if you have some olbas oil or similar in, put it in boiling water and breathe it in with a towel over your head. Works for me. It won't cure the infection, because you will need antibiotics for that, but it will hopefully stop it from sticking on your chest too much.
Worst that can happen is it get worse and you get a temperature, wheezing and pain requring an emergency appointment, if it is viral you may well start to feel better by then. dc and I recently had one which took over 3 weeks.
In my extensive experience of chest infections a cough does not a chest infection make When I have a chest infection I feel like my chest is on fire, I cannot breathe, move, eat or do anything, sometimes cough up blood and cannot stop coughing day or night.
If you dont feel that bad then I guess unfortunately you'll have to grin and bear it. If you start feeling much worse then I would try and get an emergency appointment as like pp said it can turn into pneumonia and also even just a bad chest infection can lay you low for weeks.
I have a rotten cough at the moment as well so sending you empathy. I tend to be of the 'leave it alone and it will go away' tendency; if I can walk about, eat, think in between spluttering and the odd undignified spit then there's not much to worry about.
I have had something similar recently. After two weeks, I saw the pharmacist, who gave me Night Nurse to help me sleep, as it contains a cough suppressant. Cough/cold finally went away after nearly 4 weeks.
DH once ignored a chest infection for three months, carried on cycle racing twice a week and ended up in hospital. All before he met me.
If you are concerned, do you have an NHS walk in centre near by? IME they are very good.