Hello from JustAnswer.
Yes, it is possible that there could be some residual chronic inflammation of the airways related to the illness 6 years ago. It is appropriate to perform an evaluation to be certain that there is no current issue, such as an allergy to another substance that is not as severe as the previous allergy. But if there is no current issue that is causing the symptom, then it may be a residual effect from the previous illness.
It is also possible that someone can get symptoms that act like asthma or bronchitis from other medical conditions, particularly acid reflux. You mention that you are having a rattle in the oesophagus at night, and this also could be related to acid reflux. When the refluxed acid is able to get into the lungs, it can cause wheezing, shortness of breath, chronic cough, or sputum production. Your doctor can order tests to look for acid reflux, or another option would be to try over the counter medicines to suppress stomach acid to see if it helps ease your symptoms, such as ranitidine or esomeprazole.
If I can provide any additional information, please let me know.
Acid reflux causing lung symptoms is less common than allergies, but I mention it as a possibility, particularly since you mention other oesophageal symptoms. Some people with acid reflux do not have heartburn and only have lung symptoms.
Yes, it would be appropriate to consider an allergy evaluation, including to the cats.