Brief Answer:
Needs a complete clinical correlation

Detailed Answer:
Thank you for asking
The sticky slimy sputum with mucus and cough is a multi dirctional history. Considering your age it could be an acute infection like Lower respiratory tract infection or pneumonia etc, A chronic infection like chronic bronchitis and asthma etc. May other possibilities like post nasal dripping, GERD , Aspirations, Malignancies and infections like bronchiectasis needs to be sorted out.
It needs pulmonary functions assessment and a detailed clinical correlation with some work up to sort it out. You already are on antibiotics, mucolytics and inhalers. Continue the same treatment, and let a pulmonologist help you in this regard . As to help you better , getting in to the depth is very important here.

Get a pulmonologist and let them take care of you.
I hope it helps. Take good care of yourself and dont forget to close the discussion please.
May the odds be ever in your favour.
Regards
Khan

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