Let me guide you through this process . First of all the way u have managed is pretty good as u have done most things right . One advise of mine is don’t take antibiotics without consultation . Most of the time the cough and phlegm is because of a viral infection which subsides in 5 days without the need for antibiotic . Another advise is , once u start an antibiotic make sure u give a course of at least 5 days . That way the medicine will work properly the next time u use it.
Next Steps
Don’t use the nebuliser unless prescribed . A cough syrup will do a job resonably well . Maintaining and cleaning the nebuliser should be very proper .
Health Tips
Kindly consult if this initial step doesn’t work or is ineffective so that we can plan it better