Thank you for the additional information.
Your doctor is correct that it is most likely that the original infection has precipitated some allergic inflammation. However, it is also possible that this inflammation has extended into the chest, causing an allergic bronchitis. This would be particularly true if the mucus is coming from the chest, rather than draining from the upper airways.
There are some other possibilities to consider with the symptoms that you describe. There are some rare viral
infections that can last for several months. There are also some non-allergic forms of inflammation, such as vasomotor inflammation. It is also possible that the cough and mucus is due to irritation from acid reflux. Although most people with acid reflux will have heartburn as the primary symptoms, there are some people in whom the only symptoms are related to irritation of the airways, so can cause mucus production, cough, or shortness of breath.
Since allergies are the most likely, it would be reasonable to consider the use of a steroid inhaler
addition to the steroid nose spray. In people with more significant symptoms, it also would be appropriate to consider systemic
steroids, such as oral prednisone. All of these options are only available by prescription, so would need to be discussed with your doctor.
Of the other possible conditions, the only condition that can be well managed with an over the counter medicine is the acid reflux, which will usually respond well to medicines that suppress the release of stomach acid, such as Prilosec or Prevacid. Therefore, even though it is not the most likely cause of your symptoms, it is an option to try the medicines that can be easily obtained.
If you have any further questions, please let me know.