How long have you had the cough?
Any fever?
Any nasal symptoms?
Are you now, or have you ever been a smoker?
I have had the cough, and clearing throat, for months. No fever. Sometimes nasal symptoms, sometimes not. I haven't smoked tobacco for 40 years, but I have smoked marijuana frequently for a long time, but not over once a day. I have tried to keep this a secret, i.e., I haven't told my doctor.
Your doctor needs to know that you smoke marijuana. You may have an element of smoking related disease that your doctor is not considering.
Other things to consider are a post nasal drip, using a steroid nasal spray may improve matters. Your doctor may also want to rule out acid reflux from gastro-esophageal reflux.
The fact that the mucus is white suggests that there is no actual infection and antibiotics are not warranted.
The reflux disease may be a factor and you should be doing the usual things such as raising the head of the bed, and wearing loose clothing round the waist.
Your dose of Nexium may need to be adjusted, but I would suggest you speak to a gastroenterologist first.
Pharmacist
MRPharmS. Worked as Community pharmacist for 16 years. Undertaking a second degree in medicine.