So sorry you have the cough @JoeyLiz - it is just so annoying & tiring too, if keeping you awake in the night too.
If your mucus is green - it is a chest infection & you should be on antibiotics. Cream - pale yellow mucus is usually 'normal'.
I had a similar persistent cough in the 6 months lead up to my diagnosis that I couldn't shake - and even ended up on prednisone as well as having the antibiotics earlier.
My mantra is If In Doubt Get Checked Out
Yep - I would be requesting an Xray for your own peace of mind.
Can your Breast Care Nurse assist you with getting an appointment asap?
All the best xx