Hi. Thanks for an elucidate history.
Gone through what you have written and your understanding of your problems.
Continue with Augmentin
Duo and rulide and your medicines for asthma
For the phlegm to come out , the best way is to take a good steam inhalation with plain water ( do not add anything to the boiling water) .
The steam by virtue of its mucolytic
will loosen the phlegn and can be easily be expelled. Once clear this will give you a better sleep.
Chesty can defnitely help , try this out , we want relief at any cost.. to get the soreness of the chest and abdominal muscles , a sleep and rest too.
I would advise you to talk to your Doctor if at all you require oral doses of steroid