I'm a little confused.... Steroids will generally suppress the body's own production of steroids (i.e., prednisone, cortisone).  That's why it's so important to go off them slowly.  Maybe dropping from 40 mg to 20 mg was too fast? For some people, it can be very hard to get off.  Or, maybe it's not the right thing at all.  Not the right target... did you have tests for adrenal function?

Since cortisone is an immunosuppressant, it can also 'release' infections that maybe be localized in the body.  The only parallel I can draw personally, is that before my official diagnosis of RA, I had a very stiff thumb.  When I got an injection of cortisone in that part of my hand (for the tendon - supposedly it was tendinitis, ha ha!), it cured the thumb permanents, but I got pain up my arm for 3 weeks, and ended up with a seriously damaged wrist!   Yet - I've gotten cortisone injections elsewhere in my body with no problem (jaw, shoulder, back, foot).  So - my guess (other than wanting to sue the orthopedist who did it!) is that the RA 'infection' was only in my hand, but the cortisone broke down the local immunity and allowed it to migrate. 

     Cortisone usually does help.  But what I'm thinking is, if they have not really diagnosed what you've got, the treatment may be not only not helpful, but counterproductive.  Maybe some effort should be put into determining whether it's viral, bacterial (and what kind of bacteria?  Is there any cough/spit/phlegm fluid you can give them to examine and test?)  

     I don't know, but please keep it touch, I'd like to know how this comes out, and how you are doing!  What were your upper respiratory symptoms (If i"m not being too nosy .... I am not a medical professional, just an interested friend...)