Trying to diagnose this persistent problem through a forum is very difficult.
Drainage from the nose and sinuses can be from both allergic and nonallergic causes. The nonallergic causes can be from infectious and noninfectious reasons. In your note you did not say if you have had a CT of the sinuses. When this test is normal it is unlikely to have a bacterial, fungal, or viral infection of the sinuses. If there is swelling of the lining of the sinuses, it is possible to have a low-grade infection and a culture should be done.
If this is coming from the nose, a good examination should clarify whether or not there is an infection. The symptoms you have described sound like this is more than simply worsening of your asthma.
Lastly, fungal infections can be a common problem with steroids. Doing fungal cultures of your phlegm could show if this is part of your problem.
I would suggest working closely with your doctor to get to the cause of your problem.
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