Hello and thank you for your question,
I would like to ask you a few questions to make sure I understand your situation better.
How long have you been coughing?
Do you cough all day long or does it get worse when you lay down?
How old are you?
Are you a smoker?
Do you take any medications?
Thank you for your time,
Thanks for the additional information,
There are couple of reasons you might have phlegm in your throat that you are trying to get rid of. Its possible that you have a sinus infection and the mucus from the sinuses is draining into your throat irritating it and making you want to cough up phlegm. Another reason could be cigarettes are irritating your throat and if you can, you should try not smoking for a few days to see if throat irritation improves. Another reason could be acid reflux which basically means that acid from the stomach is coming up to the throat line and causing irritation.
Since these symptoms have been going on for 3 weeks and haven't gotten better, it is best to go see your doctor because if you do have sinus infection, it should be treated with antibiotics right away.
Please feel free to follow-up with any other questions you might have. I will be happy to assist you further.
If you are satisfied with the answer, please do click 'Accept' button so that I may get credit for my work.
Best wishes and good luck,
No, it doesn't sound like a chest infection.
You said you are not coughing it up but trying to clear your throat so that makes me believe it is irritation in the throat rather then the chest.
With chest infection (like bronchitis or pneumonia) you usually have a lot of rattling in the chest with lots of coughing.